Basic Mathematics-1 Question Bank 2021-2022 PDF

A.V.C.COLLEGE (Autonomous) (Reaccredited with ‘A’ Grade by NAAC) Mannampandal – 609 305. Mayiladuthurai. PG & RESEARCH DEPARTMENT OF MATHEMATICS BASIC MATHEMATICS-I SUBJECT CODE: 21NMMA501 QUESTION BANK (From 2021-2022 onwards)...

A.V.C.COLLEGE (Autonomous) (Reaccredited with ‘A’ Grade by NAAC) Mannampandal – 609 305. Mayiladuthurai. PG & RESEARCH DEPARTMENT OF MATHEMATICS BASIC MATHEMATICS-I SUBJECT CODE: 21NMMA501 QUESTION BANK (From 2021-2022 onwards) B.Sc., Computer Science FIFTH SEMESTER.  Unit I NUMBERS 1. Which out of the following is rational number? a) 1/2 b) 6 c) 2 d) 3 2. 0.222 is a-----------------------number. a) natural b) rational c) irrational d) whole number 3) Which out of the following is a rational number? a) √3 b) √𝟒 c) √5 d) 0.333 4. If 𝜋 = 3.12158265……….then that 𝜋 is…….. a) whole number b) rational c) odd number d) irrational 5. Which of the following is Irrational number? a) 25 b) 3/4 c) 11 d) √𝟑 6. The difference between the place value and the face value of 6 in the numeral 856973 is _. a) 973 b) 6973 c) 5994 d) none of these 7. The difference between the place values of two sevens in the numeral 69758472 is. a) 0 b) 6993 c) 699930 d) none of these 8. The unit digit in the product ( 784 x 618 x 917 x 463 ) is. a) 2 b) 3 c) 4 d) 5 9. What is the unit digit in 7105 ? a) 1 b) 5 c) 7 d) 9 10. What is the unit digit in the product ( 365 x 659 x 771) ? a) 1 b) 2 c) 4 d) 6 11. What is the unit digit in ( 795 – 358)? a) 0 b) 4 c) 6 d) 7 12. If ‘a’ and ‘b’ are odd numbers, then which of the following is even? a) a+b b) a + b + 1 c) ab d) ab + 2. 13. Which one of the following number cannot be the square of a natural number? a) 30976 b) 75625 c) 28561 d) 143642 14. Which smallest number should be addid to 4456 so that the sum is completely divisible by 6 ?  a) 4 b) 3 c) 2 d) 1 15. Find the square root of 0.9 a) 0.6 b) 15 c) 3 d) None of these 16. Find the value of √0.25 a) 450 b) 0.5 c) 150 d) 5/100 17. Find the value of √40000 a) 205 b) 208 c) 200 d) 50 6 18. Find out the value of √ 3 25 a) 5/4 b) 3/5 c) 8/25 d) 9/5 19. Find out the value of √16/√0.81 a) 4/0.81 b) 400/81 c) 4/0.9 d) 4/9 20. Find out the cube root of 27/8 a) 9/2 b) 3/9 c) 2/3 d) 3/2 21. The sum of first four prime number is a) 10 b) 11 c) 16 d) 17 22. Which of the following numbers is prime a) 119 b) 187 c) 247 d) 331 23. Which of the following number is not a prime number a) 233 b) 191 c) 221 d) none of these 24. On dividing 59761 by a certain, number the quotient is 189 and the remainder is 37. Find the divisor. a) 316 b) 226 c) 353 d) none of these 25. A number when divided by 779 gives a remainder 47. By dividing the same number by19. What would be the remainder? a) 88 b) 9 c) 0 d) none of these 26. Find the number which is nearest to 30006 and exactly divisible by 29 a) 2987 b) 2900 c) 3016 d) none of these 27. What least number must be subtracted from 1000 to get a number exactly divisible by 17 a) 0 b) 3 c) 14 d) 17 28. In a division sum the divisor is12 times the quotient and 5 times the remainder. If the remainder be 48 then the dividend is a) 240 b) 576 c) 4800 d) 4848 29.The sum of two number is 25and the difference of their squares is 75.find the difference between the numbers a) 50 b) 0 c) 3 d) 8 30. If √3 = 81, then n=? a) 2 b) 4 c) 6 d) 8 31. (1-1/3) (1-1/4)…….(1-1/n) =? a) l/n b) 2/n c) 2(n-1)/n d) 2/n(n+1) 32. When simplified the product (2-1/3) (2-3/5) (2-5/7)……(2 - 997/999) is equal to a) 5/999 b) 1001/999 c) 1001/3 d) none of these 33 If a/b =4/3 then 3𝑎+2𝑏 =? 3𝑎−2𝑏 a) 6 b) 3 c) 5 d) -1 34. If x/y= 4/5 then the value of ( 4 + 2𝑌−𝑋) is 7 2𝑌+𝑋 a) 3/7 b) 1 1/7 c) 1 d) 2 35. The sum of all prime numbers between 61 and 89 is a) 610 b) 533 c) 460 d) 373 36. Which of the following is a correct statement? a) Exact value of π is 3.14 b) Exact value of 𝜋 is 22/7 c) 𝝅 is irrational d) None of these 37. If n is a natural number, then √𝑛 is a) Always a natural number b) Always a rational number c) Always an irrational number d) Sometimes a natural number and sometimes an irrational number 38. Which of the following is irrational? a) 0.14 b) 0.14161616… c) 0.14161416….. d) 0.1014001400014 39. The number p,p+2,p+4 are all primes, if p is equal to a) 3 b) 5 c) 29 d) 191 40. The product of two number is -14/27. if one of the numbers is 7/9 then the other number is a) -3/2 b) -2/3 c) 2/3 d) 3/2 41. If p is a prime number and p divides ab written as (p/ab) where a and b are integers, then a) p/a or p/b b) p/a and p/b c) p/a+b d) None 42. If P>0 and Q 0 b) p-Q> 0 𝑐) 𝑝 + 𝑄 < 0 d) p-Q< 0 43. Two numbers are in the ratio of 3:5. If each is increased by 10. The ratio becomes 5:7  the numbers are a) 3,5 b) 12,20 c) 15,25 d) 30,42 44. (243/32)-4/5 is equal to a) 16/81 b) 81/16 c) 9/2 d) 2/9 45. How many numbers between 300 and 785 are exactly divisible by 13? a) 39 b) 40 c) 41 d) None 46. The sum of first ‘n’ odd natural number is given by a) n2-1 b) (n+1)2 c) (n-1)2 d) n2 47. If the digit in the unit place of a square of natural number is 6, then the digit in the ten place will be a) 1 b) 3 c) even d) odd 48. The least prime number is a) 0 b) 1 c) 2 d) 3 49. A prime number greater then 11 will never end with a) 5 b) 7 c) 9 d) 1 50.The sum of two numbers is 15 and the sum of their square is 113. The numbers are a) 4, 11 b) 5,10 c) 6, 9 c)7, 8 UNIT -2 H.C.F & L.C.M. OF NUMBERS 1. Find the H.C.F. of 25.3, 24.3.11, 24. 32. 11 and 25.32.7 a) 6 b) 16 c) 48 d) 77 2. Find the L.C.M. of 24.3, 22.33 , 23.5.7 a) 15120 b) 4 c) 560 d) 1680 3. Find the L.C.M of 33 , 22 , 24, 3 a) 12 b) 48 c) 432 d) 108 4. Find the H.C.F of 23 , 32 , 4 and 15 a) 23 b) 32 c) 1 d) 12 5. Find the H.C.F of 42,63 and 140 a) 14 b) 9 c) 21 d) 7 6. Find the L.C.M of 22,54,108, 135 and 198  a) 330 b) 1980 c) 5940 d) 11880 7. Find the H.C.F of 1/2, 2/3, 3/4, 4/5 a) 1 b) 12 c) 4/5 d) 1/60 8. Find the L.C.M of 1/2, 2/3, 3/4, 4/5 a) 12 b) 1/60 c) 1/5 d) 1 9. Find the L.C.M of 3/4, 6/7, 9/8 a) 18 b) 3 c) 3/56 d) 9/28 10. Find the H.C.F of 1/2, 3/4, 5/6, 7/8, 9/10 a) 1/10 b) 1/120 c) 1/2 d) 9/120 11. The Product of two numbers is 1600 and the H.C.F is 5. The L.C.M of the numbers is a) 320 b) 1605 c) 1595 d) 8000 12. The H.C.F of two numbers is 16 and their L.C.M is 160. If one of the numbers is 32 then the other number is a) 48 b) 80 c) 96 d) 112 13. The H.C.F of two numbers is 4 and their L.C.M is 576. If one of the numbers is 64. then the other number is a) 48 b) 72 c) 36 d) 16 14. If H.C.F of 852 and 1491is 213 then find L.C.M a) 5964 b) 5868 c) 5694 d) 5688 15. L.C.M and H.C.F of two numbers are 60 and 3 respectively. If one number is 15, then the second number will be a) 60 b) 12 c) 20 d) 4 16. Three numbers are in the ratio 2:3:5 and their L.C.M is 240, then the greatest number will be a) 16 b) 24 c)40 d) 120 17. Sum of the two numbers is 56 and their L.C.M. is 105 then the H.C.F. of numbers will be a) 7 b) 8 c) 4 d) 5 18. The sum of two numbers is 64 and their H.C.F. is 8 then find the possible pair of numbers? a) 16,48 b) 8,56 c) 32,32 d) none 19. The product of two numbers is 2160 and their H.C.F is 12 then find the possible pair of numbers? a) (144,15) b) (60,12) c) (36,60) d) none 20. Find the least number which on dividing by 10,12 and 15 leaves remainder as 3 in each case. a) 63 b) 123 c) 183 d) 243 21. Find the greatest number which on dividing by 166,199 and 298 will leave the same remainder in case. a) 11 b) 33 c) 99 d) 3 22. Find the smallest number which on dividing by 10,12 and 15 will leave remainders as 9,11 and 14 respectively. a) 59 b) 119 c) 179 d) 249 23. Find the least number which on dividing by 8,12,16 leaves remainder as 3 but it is completely divisible by 7? a) 63 b) 51 c) 99 d) 147 24. Find the greatest number which on dividing 185,225 and 395 leaves remainder as 3,4 and 5 respectively? a) 13 b) 12 c) 11 d) 17 25. Find the greatest number of 4 digits which on dividing by 10,12,15 will leaves remainder as 3, in each case? a) 9963 b) 9693 c) 9936 d) 9369 26. Find the smallest whole number which is exactly divisible by 11/2, 11/3, 21/4, 31/4, and 41/5 a) 3276 b) 126 c) 315 d) 405 27. Find the H.C.F. of 2.4, 0.36 and 7.2 a) 1.2 b) 0.12 c) 12 d) 120 28. L.C.M. of 2/5, 3/10 and 6/25 is a) 3/25 b) 6/5 c) 1/15 d) 12/25 29. The least number by which 2 x 6 x 7 x 7 should be multiplied to make a perfect square is a) 2 b) 3 c)6 d) 7 30. What is the least number which when divided by 4,5,6 and 8 leaves a remainder 3 but when divided by 9 leaves no remainder? a) 123 b) 243 c) 729 d) 363 31. In finding the H.C.F. of two numbers the least divisor is 41 and the quotients from first to last are 2,4 respectively. The numbers are a) 700 and 400b) 800 and 500 c) 820 and 369 d) 820 and 360 32. Three numbers are in the ratio 1:2:3 and their H.C.F. is 12. The numbers are  a) 12, 24, 36 b) 10, 20, 30 c) 5, 10, 15 d) 4,8,12 33. The H.C.F and L.C.M. of two numbers are 50 and 250 respectively. If the first number is divided by 2, the quotient is 50. The second number is a) 50 b) 100 c) 125 d) 250 34. Find the least number of square tiles required to cover a floor 180m long and 105 broad. a) 15 b) 12 c) 84 d) 180 35. Three bells ring together at intervals of 12,15 and 18 sec. respectively, then how many times do they ring together in one hour if they start simultaneously? a) 20 b) 21 c) 40 d) 41 36. Traffic light at one particular crossing changes after every 32 and 40 seconds. The traffic light at a certain time changes together. After what time will they again change together? a) 2 min.40 sec. b) 1 min :20 sec. c) 3 min :20 sec. d) 2 min. 20 sec. 37. The traffic lights at three different roads crossing change after every 48 sec., 72 sec. and 108 sec. respectively. If they all change simultaneously at 8:20:00 hours. They will again change simultaneously at a) 8:27:12 hrs. b) 8:27:36hrs. c) 8:27:24hrs. d) 8:27:48hrs. 38. Six bells commences tolling together and toll at intervals 2, 4, 6,8,10 and 12 seconds respectively. In 30 Minutes, how many times do they toll together? a) 4 b) 10 c) 15 d) 16 39. An electronic device makes a beep after every 60 sec. Another device makes a beep after every 62 sec. They beeped together at 10A.M. The time when they will best make a beep together at 10 A.M. The time when they will nest make a beep together at the earliest is a) 10.30A.M. b) 10.31A.M. c) 10.59A.M. d) 11A.M. 40. The L.C.M. of 10,12,15 is a) 60 b) 75 c) 120 d) 180 41. Find the highest common factor of 851 and 943 a) 280 b) 420 c) 140 d) 23 42. The L.C.M. of two numbers is 840 and their H.C.F. is 14 if one of the numbers is 42, find the other a) 280 b) 410 c) 150 d) 88 43. Find the least number which when divided by 12,18,36,45 leaves the remainders 8,14,32 and 41 respectively  a) 176 b) 180 c) 178 d) 186 44. What is the smallest number which when divided by 5,10,12 and 15 leaves remainder 2 in each case but when divided by 7 leaves nothing? a) 189 b) 182 c) 175 d) 91 45. What is the least number which when divided by 6 leaves 5, When divided by 7 leaves 6 and when divided by 8 leaves to 7? a) 173 b) 170 c) 166 d) 167 46. Find the smallest number which if divided by 4,9,12 and 16 each time 3 remains a) 290 b) 141 c) 147 d) 146 47. Two numbers are in ratio of 15:11 if their H.C.F. is 13, then the numbers are a) 75,55 b) 105,77 c) 15,11 d) 195,143 48. The largest number which divides 25,73 and 97 to leave the same remainder in each case is a) 24 b) 23 c) 21 d) 6 49. Find the H.C.F of 23 x 32 x 5 x 74 , 22 x 35 x 52 x 73 , 23 x 53 x 72 a) 890 b) 980 c) 809 d) 908 50. The H.C.F. of 2/3, 8/9, 64/81, and 10/27 is a) 2/3 b) 2/81 c) 160/3 d) 160/81 UNIT – 3 AVERAGE 1. If 100 typists typed 4521 pages in 10 hours, then the number of pages types per hours by an average typist is a) 4.21 b) 4.25 c) 4.52 d) 4.53 2. Average price of 4 books is Rs.18. Which of the following could be the possible price of one of the books? a) Rs.70 b) Rs.73 c) Rs.76 d) Rs.78 3. Chandramohan travels on a cycle at the rate of 10kms. Per hour for 2 hours and at the rate of 9kms. Per hour for 3 hours. His average speed is a) 9.1kms/hr b) 9.2kms/hr c) 9.4kms/hr d) 9.6kms/hr 4. The average of even numbers from 1 to 20 is a) 10 b) 11 c) 12 d) 110 5. The average of the first six prime numbers is  a) 6.50 b) 6.83 c) 9.33 d) 41 6. The average length of the four sides of a trapezium of length 10cms, 16cms, 14cms and 18cms is a) 8cms b) 20cms c) 22cms d) None of these 7. The average of 8numbers is 8, and the average of another 4 numbers is 6, the average of all the numbers is a) 8.33 b) 7.33 c) 7.66 d) 9.33 8. The average age of 30 boys in a class is 16 years. The average of the ages of the boys and the teacher is 17 years. The age of teacher is a) 17 years b) 30 years c) 33 years d) 47 years 9. The average age of a group of 12 boys is 12 years. When three more boys joined the group, the average age increased by 3 years. The sum of the ages of the three new boys is a) 36 years b) 45years c) 81years d) 144 years 10. The average age of 5 boys is 12. The average age of other 3 boys is 16. The average age of all the 8 boys is a) 11.5years b) 12.5years c) 13.5years d) 14.5years 11. The average of 4, 5, 4.5, 6.5, 8.5 and 6 is a) 5.25 b) 5.70 c) 5.57 d) 5.75 12. The average of five consecutive even numbers starting with 4 is a) 4 b) 7 c) 8 d) 9 13. The age of five boys are 5, 8, 11, 12 and 14 years. Their average age is a) 13 years b) 12 years c) 10 years d) 8 years 14. The average of seven numbers is 5, and average of first six number is 4. The seventh number is a) 22 b) 2 c) 11 d) 12 15. The average of nine numbers is 12. If each number is increased by 2, the average of the new set of numbers is a) 12 b) 13 c) 14 d) 15 16. The average weight of a class of 24 students is 35kg. If the weight of the teacher be included, the average increased by 400gms. Find the weight of the teacher a) 40k.g b) 42k.g c) 45k.g d) 48k.g 17. The average of 6 observations is 12. A new seventh observation is included and the  new average is decreased by 1. The seventh observation is a) 1 b) 3 c) 5 d) 6 18. The average weight of 19 students is 15k.g. By the admission of a new student, the average weight is reduced to 14.8kg. The weight of the new student is a) 10.6kg b) 10.8kg c) 11kg d) 11.9kg 19. The average age of an adult class is 40 years. 12 new students with an average of 32 years join the class, thereby decreasing the average by 4 years. The original strength of the class was a) 10 b) 11 c) 96 d) 15 20. The average height of 30 girls out of 40 is 160 c.m and that of the remaining girls is 156 c.m. The average height of the whole class is a) 158c.m b) 158.5c.m c) 159c.m d) 159.5c.m 21. A batsman makes a score of 87 runs in the 17th inning and thus increased his average by 3. Find his average after 17th inning. a) 39 b) 87 c) 70 d) 42 22. The average of 30 results is 20 and the average of other 20 results is 30. What is the average of all the results a) 24 b) 25 c) 48 d) 50 23. The average of five results is 46 and that of the first four is 45. The fifth result is a) 40 b) 10 c) 42.5 d) 50 24. Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 56, the three numbers in order are a) 48,96,24 b) 48,24,96 c) 60,30,120 d) 120,60,30 25. The average of three numbers is 42. The first is twice the second and the second is twice the third. The difference between the largest and smallest number is a) 18 b) 36 c) 54 d) 72 26. The average score of a cricketer for 10 matches is 43.9 runs. If the average for the first six matches is 53, the average for the last four matches is a) 17.15 b) 29.75 c) 30.25 d) 31 27. The average of 50 numbers is 38. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is a) 36.5 b) 37.0 c) 37.5 d) 37.52 28. The average age of three boys is 15 years. If their ages are in the ratio 3:5:7, the age of the youngest boy is a) 9 b) 15 c) 18 d) 21 29. Ram goes to his office on foot at the rate of 8 km. per hour but returns home in auto- rickshaw at the rate of 12 km/hr. What is the average speed? a) 20 km b) 21 km c) 40 km d) 9.6 km 30. Seven men agree with 8th man to subscribe a sum of money for a chit fund. The first seven are to subscribe Rs. 50 each and 8th man Rs. 70 more than the average of all the eight. Find how much did the 8th man subscribe. a) Rs. 130 b) Rs. 21 c) Rs. 40 d) Rs. 41 31. A man engaged another man for 40 days on the condition that he would pay him Rs.20 for each day he works and would take from him Rs. 10 for each absence. At the end of 40 days the servant was paid Rs. 500. Find how many days he was absent. a) 20 b) 21 c) 10 d) 41 32. The average age of father and son is 40 years the average age of father and mother is 54 years and the average age of mother and son is 38 years. Find the average age of father, mother and son. a) 20 b) 21 c) 40 d) 44 33. The average of first five multiple of 3 is a) 27 b) 12 c) 9 d) 3 34. The average of run made by Raju, Shyam and Hari is 7 less than that made by Shyam, Hari and Kishore. If the number of Kishore’s run is 35. What is Raju’s run? a) 7 b) 14 c) 21 d) 35 35. A batsman has a certain average runs for 10 innings. In the 11th inning he scored 50 runs thereby increasing his average by 4 runs. What is his average after 11th inning? a) 11 b) 8 c) 10 d) 9 36. If Anil goes to school from his home by an average speed of 5 km an hour, he reaches there at the correct time. If however his average speed is 4 km an hour he reaches there 15 minutes late. Find the distance of the school from his home a) 4.5km b) 6km c) 5km d) 3km 37. Nine men went to a hotel. Eight of them spent Rs.3 each over their meals and 9th spent Rs. 2 more than the average of all the nine. Find the total money spent by them a) Rs.28.50 b) Rs.27.30 c) Rs.29.25 d) Rs.30.50 38. A motorist completes the journey between A and B at a constant speed 20km/h and covers the return journey from B to A at constant speed 30 km/h. What was the average speed. a) 50 km/h b) 26 km/h c) 60 km/h d) 24 km/h 39. My average expense for 4 days is Rs 6.00. I spend Rs 7.70 on first day, Rs. 6.30 on second day. If I spend Rs.10 on third day, what did I spend on 4th day? a) Rs.2 b) Rs.4 c) Rs.3 d) None of these 40. The average score of a cricket player for five innings is 20. If he scored 14,30,40 and 10 in 4 innings, how many runs did he score in fifth inning? a) 6 b) 20 c) 10 d) 26 41. Abdul sold 1800 in the first month and 2580 articles in the second month. How many articles should he sell in the third month so that his average sale in the 3 months would be 2300 articles? a) 2190 b) 2520 c) 2420 d) 3340 42. The average age of a class was 16 years. But 4 boys whose average age was 13 years and 6 months were admitted. The class average was 15 years and 7 months. How many boys were there after the new admission? a) 24 b) 16 c) 21 d) 29 43. The average age of 5 students is taken today. It is 14 years. How much it will be if taken after 5 years? a) 17 years b) 19 years c) 20 years d) 25 years 44. A man had 5 children. When their average age was 10 years the child who was 5 years of age died. What was the average age of surviving children 4 years after the death of child. a) 15 ¼ years b) 14¾ years c) 15 years d) 14 years 45. Yogesh travels 48 km at 12km/hr and a further 48 km at 16km/hr find his average speed for whole journey. a) 13 4/7 km/hr b) 12 5/7 km/hr c) 12 4/7km/hr d) 13 5/7 km/hr 46. The average weight of a group of boys and girls is 38 kg. the average weight of the boys is 42 kg and that of the girls is 33 kg. If the number of boys is 50. Find the number of girls. a) 44 b) 40 c) 48 d) 50 47. The average salary of Rajesh, Shyam and Manoj is Rs.800 and the average salary of Shyam, Piyush and Manoj is Rs.900 and Piyush’s salary is Rs.900. What is Rajesh’s salary? a) Rs.600 b) Rs.500 c) Rs.400 d) Rs.900 48. The average of the incomes of Gopal, Harish and Salil is Rs.1500 if the average of Gopal and Harish’s income is Rs.1000. what is the income of Salil? a) Rs.2000 b) Rs.3500 c) Rs.2500 d) Rs.3300  49. A family consists of grandparents, parents and three grand children. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grand children is 6 years. What is the average age of the family? a) 28 4/7 b) 31 5/7 c) 32 1/7 d) None of these 50. Out of 9 persons , 8 persons spent Rs.30 each for their meals. The ninth one spent Rs.20 more than the average expenditure of all the nine. The total money spent by all of them was (a) 260 (b)290 (c)292.50 (d)262.50 UNIT – 4 RATIO AND PROPORTION 1. The ratio of 60 kg to 1.5 quintals is (a)4:1 (b)2:5 (c)5:2 (d)4:5 2. The ratio of 3.5 kg to 280 gm is (a)2:25 (b)4:5 (c)25:2 (d) 5:4 3. If the following ratio 2:9, 3:11, 5:13, 3:7 the greatest ratio is (a)2:9 (b)3:11 (c)5:13 (d)3:7 4. The compound ratio of 3:4, 8:15, 25:28 is (a)3:28 (b)5:14 (c)14:5 (d)28:3 5. The least ratio among the following ratio 5:6, 7:8, 2:3, 9:17 is (a) 5:6 (b)7:8 (c)2:3 (d)9:17 6. The ratio of daily wages of A and B is 4:5. Their total daily wages is Rs.45. A’ s Share will be (a)Rs.20 (b)Rs.25 (c)Rs.15 (d)Rs.30 7. If A:B=2:3;B:C=4:5,C:D=6:7 then A:D is (a)2:7 (b)16:35 (c)17:35 (d)18:35 8. If A:B=3:4;B:C=5:6,C:D=8:9 then A:B: C:D is (a)15:24:20:27 (b)24:27:20:15 (c)15:20:24:27 (d)27:24:20:15 9. The number which bears the same ratio to 49 as 56 bears to 98 is (a)28 (b)56 (c)84 (d)98 10. The fourth proportional to 12, 18 ,26 is (a)24 (b)36 (c)39 (d)49 11. The first proportional to 10,24,6 is (a)1 (b)20 (c)40 (d)5 12. The second proportional to 1/2, 1/4, 1/6 , is (a)1/2 (b)1/3 (c)1/4 (d)1/5 13. The value of x for which 3 1⁄3 , 5 5⁄6 , x, 12 1⁄4 are in proportion is (a)7 (b)8 (c)9 (d)1 14. The mean proportional to 21 and 105is (a) 63 (b) 𝟐𝟏√𝟓 (c) 21√3 (d) 21√7 15. The number which must be added to each of 6, 8, 11,14 so that these become proportional is (a)1 (b)2 (c)3 (d)4 16. Divide Rs.455 in the ratio 4:3 (a) 250:205 (b)260:195 (c)195:260 (d)205:250 17. If A:B = 2:3 and B:C = 4:5 then C:A is equal to (a) 15:8 (b) 12:10 (c) 8:5 (d)11:7 18. If A:B = 5:7 and B:C =6:11 then A:B:C is (a) 55:77:66 (b)30:42:77 (c)35:49:42 (d)None of these 19. If A:B = 2:3 and B:C =4:5 then C:D = 6:7 then A:D is equal to (a) 2:7 (b) 7:8 (c) 16:35 (d)4:13 20. If X:Y = 2:3 and 2:X = 1:2 then value of y is (a) 4 (b) 6 (c)1/3 (d)3/2 21. If A = B/3 and B = C/2 then A:B:C is (a) 1:3:6 (b) 2:3:6 (c) 3:2:6 (d) 3:1:2 22. If 2A = 3B = 4C then A:B:C is (a) 2:3:4 (b)4:3:2 (c)6:4:3 (d)3:4:6 23. If 2A = 3B and 4B = 5C then A:C is (a) 3:4 (b) 8:15 (c)15:8 (d)4:3 24. In a mixture of 35 litres, the ratio of milk and water is 4:1. Now, 7 litres of water is added to the mixture. Find the ratio of milk and water in the new mixture. (a) 5:1 (b) 4:8 (c) 2:1 (d)5:8 25. A mixture contains alcohol and water in the ratio 4:3. If 7 litres of water is added to the mixture the ratio of alcohol and water becomes 3:4. Find the quantity of alcohol in the mixture. (a) 9 litres (b)10 litres (c) 11 litres (d)12 litres. 26. Two numbers are in the ratio 3:5. If each number is increased by 10, the ratio becomes 5:7. The numbers are (a) 3,5 (b)7,9 (c) 6,10 (d)15, 25. 27. A bag contains 1 rupee , 50 paise and 25 paise coins in the ratio 5:6:8. If the total amount is Rs.420 find the number of coins of each type. (a)208, 256, 336 (b) 210, 252, 336 (c) 212,252, 328 (d)210, 256, 328. 28. Find three numbers in the ratio 2:3:5 , the sum of whose squares is 608. 2 3 5 (a) 20, 30, 50 (b) , , (c) 8, 12, 20 (d)1,2,3. 608 608 608 29. A bag contains 30 coins of 50 paise and 25 paise. The ratio of their values is 1:2.Find the number of coins of 50 paise. (a) 5 (b) 6 (c)10 (d)7 30. Find the fourth proportional of 6,7 and 12 (a)10 (b) 12 (c)14 (d)18. 31. What should be added to the term of ratio 9:16 to get 2:3 (a) 10 (b)5 (c)1 (d)4 32. 25 men working of 6 hours a day can do a price of work in 36 days find how many men working 8 hours a day. Do the same work in 45 days? (a) 5 (b) 6 (c)10 (d)15 33. 11 chairs cost as much as 3 tables. A chair and a table cost Rs.140. What does a chair cost? (a) Rs.110 (b) Rs.30 (c)Rs.70 (d)Nothing 34. Ratio of vijay’s age to Vivek’s is equal to 10:9. If vijay will be 26 years old after 6 years.Find the present age of vivek? (a) 18 years (b) 20 years (c) 27 years (d)22 ½ years. 35. If A:B = 3:4 , B:C = 6:9 , C:D = 12:19 then A:B:C:D is (a) 9:12:16:19 (b)9:12:18:19 (c)6:8:12:19 (d)3:4:8:19 36. What is the weight of 5 metres of a uniform iron rod , if 13 metres of it weight 23.4 kg? (a) 9 Kg (b)10 Kg (c)4.68 Kg (d)6.5 Kg 37. ‘X’ , ‘Y’ , ‘Z’ , purchased mangoes in ratio of 5:3:2 if the total number of mangoes of ‘Y’ and ‘Z’ is 60. Find the number of mangoes if ‘X’. (a) 40 (b)80 (c)100 (d)60 38. The ratio of volume of two spheres is 1:8. Then the ratio of their surface areas will be (a) 1:2 (b)1:4 (c)1:8 (d)1:16. 39. The ages of Ram and Shyam are in the ratio of 2:1. After 5 years the ratio of their ages will be 3:2. Their present ages are (a) 20,10 (b)40,5 (c)15,5 (d)10,5 40. A bag contains 50p, 25p coins ratio of 5:6:7. If the total amount is Rs.390.find the total number of coins (a)600 (b) 660 (c)700 (d)720 41. Two numbers are in the ratio 3:5. If 9 is added to each , then they are in the ratio 12:23.The second number is (a)50 (b) 55 (c)54 (d)53 42. Between two railway station I,II,III class fares are in ratio of 10:8:3 and the number of passengers for I,II,III CLASSES was 3:4:10 respectively. If the total sales of tickets during that year was Rs.8280. Then the amount collected from II class fares (a)Rs.2800 (b)Rs.2980 (c)Rs.3080 (d)Rs.2880. 43. Divide Rs.258 in 8 men , 6 women and 10 children such that a women gets 3/2 of a child and a man gets twice of a women. Then find the share of each man? (a) Rs.6 (b) Rs.9 (c)Rs.18 (d)Rs.3 44. The ratio of milk and water in 20 litres mixture is 3:1. How much milk must be added so that the ratio becomes 4:1? (a) 4 ltrs (b) 5 ltrs (c)8 ltrs (d)10 ltrs 45. In a factory the ratio of male workers to female workers was 5:3. If the number of female workers was less by 40. What was the total number of workers in the factory? (a) 100 (b) 500 (c) 160 (d) 200 46. The mean proportion of 0.32 and 0.02 is  (a) 0.16 (b) 0.30 (c)0.34 (d)0.08 47. Ratio between the annual incomes of Mahavir and Suresh is 5:4 and between their expenditure is 3:2. If at the end the year both save Rs.800 each, find the income of Mahavir (a)Rs.1600 (b)Rs.1400 (c)Rs.2000 (d)Rs.2400 48. Rs.800 were divided between Mahesh and Shyam in ratio 3:5. How many rupees more will Shyam get than Mahesh? (a) 40 (b) 90 (c)100 (d)200 49. Four men or 6 women take 12 days to do a job. How many days will 3 men and 4 women together take to do the same job? 𝟖 13 (a) 𝟖 (b) (c) (d) 8 𝟏𝟕 1 11 17 9 8 17 17 50. In a bag there are coins of 25 paise , 10 paise and 5 paise in the ratio of 1:2:3 if there are in all Rs. 30 in the bag ; how many coins of 5 paise are there ? (a) 5 (b) 100 (c) 125 (d)150 UNIT – V PROBLEMS ON TRAINS 1. A train 100m long is running at the speed 30km/hr. Find the time taken by it to pass a man standing near the railway line (a) 11 seconds (b) 12 seconds (c) 13 seconds (d) 18 seconds 2. Two trains 137 m and 163 m in length are running towards each other on Parallel lines, one at the rate of 42 kmph and another at 48 kmph. In what time will they be clear of each other from the moment they meet? (a) 13 seconds (b) 12 seconds (c) 10 seconds (d) 7 seconds 3. A man sitting in a train which is travelling at 50 kmph observes that a goods train, travelling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed (a) 254 km ph (b) 134 km ph (c) 62 km ph (d) 112 km ph 4. How long does a train 110 m long running at the speed of 72 km/hr take to cross a bridge 132 m in length? (a) 9.8 sec (b) 12.1 sec (c) 12.42 sec (d) 14.3 sec 5. A train 138 m long passes a telegraph pole in 6 seconds. Find the speed of the train. (a) 70 km/hr (b) 72 km/hr (c) 79.2 km/hr (d) 82.8 km/hr 6. A train 800 m long is running at a speed of 78 km/hr. If it crosses a Tunnel in 1 minute, then the length of the tunnel (in meters) is: (a) 130 (b) 360 (c) 500 (d) 540 7. A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train? (a) 69.5 km/hr (b) 70 km/hr (c) 79 km/hr (d) 79.2 km/hr 8. A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? (a) 5 sec (b) 6 sec (c) 7 sec (d) 10 sec 9. Two trains are moving in opposite direction at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is: (a) 36 (b) 45 (c) 48 (d) 49 10. Two trains are running in opposite direction with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is : (a) 10 (b) 18 (c) 36 (d) 72 11. Two trains are running at 40 km/hr and 20 km/hr respectively in the Same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train? 2 𝟕 (a) 23 m (b) 23 m (c) 27 m (d) 𝟐𝟕 m 9 𝟗 12. A train 150 m long passes a km stone in 15 seconds and another train of the same length travelling in opposite direction in 8 seconds. The speed of the second train is :  (a) 60 km ph (b) 66 km ph (c) 72 km ph (d) 99 km ph 13. A speed of 90 kmph is same as (a) 25 m/s (b) 20 m/s (c) 22 m/s (d) 30 m/s 14. A train 245m long, running with a speed of 63 km/hr will pass a tree in (a) 14 sec (b) 16 sec (c) 18 sec (d) 20 sec 15. A 300 m long train crosses a platform in 39 seconds while it crosses a signal pole in 18seconds. What is the length of the platform? (a) 320 m (b) 350 m (c) 650 m (d) none of these 16. A train 125 m long passes a man, running at 5 kmph in the same direction in which the train is going, in 10 seconds. The speed of the train is: (a) 45 km/hr (b) 50 km/hr (c) 54 km/hr (d) 55 km/hr 17. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? (a) 9 a.m. (b) 10 a.m. (c) 10.30 a.m. (d) 11 a.m. 18. A train 100 metres long takes 5 seconds to cross a man walking at 5 kmph in a direction opposite to that of the train. Find the speed of the train. (a) 54 kmph (b) 35 kmph (c) 67 kmph (d) 55 kmph 19. A train moves with a speed of 108 kmph. Its speed in metres per second is (a) 10.8 (b) 18 (c) 30 (d) 38.8 20. A speed of 14 metres per second is the same as: (a) 10 (b) 28 (c) 20 (d) None of these 21. A train 280 m long, running with a speed of 63 km/hr will pass a tree in: (a) 15 sec (b) 16 sec (c) 18 sec (d) 20 sec 22. In what time will a train 100 metres long cross an electric pole, if its speed 144 km/hr. (a) 2.5 seconds (b) 4.5 seconds (c) 5 seconds (d) 12.5 seconds 23. The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is (a) 200 m (b) 225 m (c) 245 m (d) 250 m 24. A goods train runs at the speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in metres) is: (a) 130 (b) 360 (c) 500 (d) 540 25. A train travelling at a speed of 75 mph enters a tunnel 3 /21miles long. The train is ¼ mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges? (a) 2.5 min (b) 3 min (c) 3.2 min (d) 3.5 min 26. A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train in km/hr? (a) 69.5 km/hr (b) 70 km/hr (c) 79 km/hr (d) 79.2 km/hr. 27. A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger? (a). 3.6 sec (b). 18 sec (c). 36 sec (d). 72 sec 28. Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is (a) 2:3 (b) 4:3 (c) 6:7 (d) 9:16 29. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? (a) 9. am (b) 10.a.m (c) 10.30 a.m (d) 11.a.m 30. A train X starts from Meerut at 4 PM and reached Delhi at 5 PM. While another train starts from Delhi at 4 PM and reaches Meerut at 5:30. The two train will cross each other at ? (a) 4.36 p.m (b) 4:48 a.m (c) 4.42 p.m (d) 4.50 p.m 31. A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? (a) 40 sec (b) 42 sec (c) 45 sec (d) 48 sec 32. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?  (a)120 metres (b) 180 metres (c) Cannot be determined (d) None of these 33. A train X speeding with 120 kmph crosses another train Y, running in the same direction in 2 minutes. If the lengths of the train X and Y be 100 m and 200 m respectively, what is the speed of train Y? (a) 111km/hr (b) 123 km/hr (c)127 km/hr (d) 129 km/hr 34.. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speed is: (a) 1 : 3 (b) 3 : 2 (c) 3 : 4 (d) None of these 35. A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is (a) 400 m (b) 450 m (c) 560 m (d) 600 m 36. A train covers a distance of 12 km in 10 minutes. If it takes 6 seconds to pass a telegraph post then the length of the train is: (a) 90 m (b) 100 m (c) 120 m (d) 140 m 37. A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is : (a) 50 m (b) 150 m (c) 200 m (d) Data inadequate 38. The length of a train and that of a platform are equal. If what a speed of 90 km/hr, the train crosses the platform in one minute, then the length of the train(in metres): (a) 500 (b) 600 (c) 750 (d) 900 39. The train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? (a) 120 m (b) 240 m (c) 300 m (d) None of these 40. A train of 240 m long passed a pole in 24 seconds. How long will it take to pass a platform 650m long? (a) 65 sec (b) 89 sec (c) 100 sec (d) 150 sec 41. A train crosses a platform 100 m long in 60 seconds at a speed of 45 km/hr. The time taken by the train to cross an electric pole is: (a) 8 sec (b) 52 sec (c) 1 minute (d) Data inadequate 42. A goods train runs at the speed of 72 kmph and crosses a 250 m long platform is 26 seconds. What is the length of the goods train?  (a) 230 m (b) 240 m (c) 260 m (d) 270 m 43. A train of length 150 metres take 40.5 seconds to cross a tunnel of length 300 metres. What is the speed of the train in km/hr? (a) 13.33 (b) 26.67 (c) 40 (d) 66.67 44. A train takes 18 seconds to pass completely through a staion 162 m long and 15 seconds through another station 120 m long. The length of the train is: (a) 70 m (b) 80 m (c) 90 m (d) 100 m 45. A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? (a) 230 m (b) 240 m (c) 260 m (d) 320 m 46. How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? (a) 25 (b) 30 (c) 40 (d) 45 47. Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36km/hr. The faster train passes the slower train in 36 seconds. The length of each train is : (a) 50 m (b) 72 m (c) 80 m (d) 82 m 48. Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The times (in seconds) which they take to cross in seconds is: (a) 9 (b) 9.6 (c) 10 (d) 10.8 49. Two goods train each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one. (a)12 sec (b) 24 sec (c) 48 sec (d) 60 sec 50. Two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 45 kmph respectively. In how much time will they cross each other, if they are running in the same direction? (a) 72 sec (b) 132 sec (c) 192 sec (d) 252 sec X X X X X