Chapter 11 to 12 PDF

CHAPTER 11 AVERAGE Example 2. Rahul Dravid in his12th inning makes a score Average of 63 runs and thereby increase his average score by 2. The average (or mean) of a given ob...

CHAPTER 11 AVERAGE Example 2. Rahul Dravid in his12th inning makes a score Average of 63 runs and thereby increase his average score by 2. The average (or mean) of a given observation or data What is his average after the 12th inning? is a number which is found on dividing the sum of observations or data by the number of observations (1) 50 (2) 41 (3) 25 (4) 30 or data given. Sol. (2) Let the average of Dravid’s 11 innings be x. Sum of observations Then, the average of 12 innings = x + 2 Average = 11x + 63 Number of observations ∴ = x + 2 ⇒ 12 x + 24 = 11x + 63 ⇒ x = 39 12 If x1 , x2 , x3 , … , xn are n numbers, then the average of Hence, the average of 12 innings = 39 + 2 = 41 x + x2 + x3 + … + xn these numbers is x = 1 n Example 3. The average of 5 numbers is 496. If two of them are 117 and 140, find the average of remaining Example 1. The marks obtained by a student are 40 , 50 , three numbers. 60 , 70 , 80. Find his average marks. (1) 239 (2) 717 (1) 60 (2) 50 (3) 741 (4) 637 (3) 40 (4) 30 Sol. (3) Sum of 5 numbers = 496 × 5 = 2480 Sol. (1) Average marks 40 + 50 + 60 + 70 + 80 Sum of two given numbers = 117 + 140 = 257 = Sum of remaining 3 numbers = 2480 − 257 = 2223 5 2223 = 300 = 60 ∴ Average of these 3 numbers = = 741 5 3 Entrance Corner 1. The mean of 20 observations was found to 3. The average of 20 values is 18. If 3 is be 65 but later on it was found that 69 was subtracted from each of the values, then misread as 96. Find the correct mean. the new average will be [JNV 2017] [JNV 2017] (1) 21 (2) 15 (1) 63.65 (2) 12.37 (3) 16 (4) 17 (3) 69.50 (4) 65.95 4. The average of 4 numbers is 7. If the sum 2. Find the average of the following set of of first 3 numbers is 20, find the fourth scores 567, 434, 323, 290, 401 [JNV 2017] number. [JNV 2012] (1) 398 (2) 412 (1) 7 (2) 10 (3) 407 (4) 403 (3) 9 (4) 8 82 Navodaya Vidyalaya (Class VI) Entrance Exam 5. Find the average of the following numbers. 17. The average of 4, 5, 3.5, 7.5, 9.5 and 6.5 is 06, 0, 12, 14, 13 [JNV 2012] [JNV 1997] (1) 9 (2) 7 (3) 12 (4) 11 (1) 6.0 (2) 5.2 (3) 5.5 (4) 5.0 6. The average of the height of 5 students 18. The average of 3 numbers is 24. If one of having height 30, 40, 50, 60, 70 is the numbers is 18 and the other is 29, find [JNV 2011] the third number. [JNV 1996] (1) 40 (2) 50 (3) 55 (4) 45 (1) 24 (2) 25 (3) 26 (4) 27 7. The average score of a cricketer in 19. In a family consisting of 10 persons 2 matches is 27 and in 3 other matches is father, mother and the eldest son earn 32. Then, his average score in all the ` 4000, ` 3000 and ` 4400 per month. 5 matches is [JNV 2011] What is the average monthly income of a (1) 28 (2) 29 (3) 30 (4) 31 family member? [JNV 1996] (1) ` 1260 (2) ` 1600 8. The average of 20 values is 18. If 3 is (3) ` 1140 (4) ` 3800 subtracted from each of the values, then the new average will be [JNV 2009] 20. Average score in 10 matches of a cricket (1) 21 (2) 15 (3) 16 (4) 17 player was 45.6 runs. If the average score in first 6 matches was 48 runs, find the 9. The average age of 4 children is 11yr. If the average score in last 4 matches. [JNV 1995] ages of 3 children are 9 yr, 12 yr and 10 yr, (1) 42 runs (2) 44 runs find the age of the fourth child. [JNV 2001] (3) 46 runs (4) 48 runs (1) 12 yr (2) 24 yr 21. The average of 5 consecutive even (3) 13 yr (4) None of these numbers, starting with 2 is [JNV 1995] 10. The average of the first 5 even-numbers is (1) 4 (2) 6 (3) 7 (4) 5 [JNV 2001] 22. The lengths (in m) of 5 pieces of a string (1) 4 (2) 5 (3) 6 (4) 7 are 5, 5.2, 6.3, 7.2, 6.3. The average length 11. Find the average of 3, 5, 7, 8, 9. [JNV 2000] (in m) of a piece is [JNV 1995] (1) 6 (2) 6.4 (3) 7.4 (4) 8.4 (1) 5.8 (2) 6.0 (3) 6.1 (4) 6.2 12. The average of 3 numbers is 10. If the 23. The average expenditure of a man for first average of first 2 numbers is 9, find the 7 months is ` 800 and for the next 5 third number. [JNV 2000] months is ` 900. Find his average monthly expenditure. [JNV 1994] (1) 12 (2) 13 (3) 14 (4) 15 2 (1) ` 600 (2) ` 700 (3) ` 800 (4) ` 841 13. Find the average of 10, 9, 8, 7 and 6. 3 [JNV 1999] 1 1 1 1 24. Find the average of , , ,. (1) 6 (2) 7 (3) 8 (4) 9 2 4 6 8 [JNV 1994] (1) 0.26 (2) 4.17 (3) 4.18 (4) 4.19 14. Average of 2 numbers is 17. If 1 number is 21, find the other number. [JNV 1999] 25. Average of 8, 6, 0, 9 and 7 is [JNV 1994] (1) 7 (2) 8 (3) 12 (4) 13 (1) 6 (2) 8 (3) 3 (4) 5 15. The average age of a group of 5 boys is 26. Average of class I to class V is 29. Average 15 yr. If an other boy of 15 yr joins them, of class I to class III is 31. Average of class IV to class V is [JNV 1993] find the average of the whole group. (1) 25 (2) 26 [JNV 1998] (3) 27 (4) 28 (1) 14 yr (2) 16 yr (3) 17 yr (4) 15 yr 27. Marks obtained by 10 students are 23, 25, 16. The heights of 5 students are 140, 135, 37, 36, 27, 28, 29, 34, 36, 38. The average 142, 138, 140. Their average height is marks are [JNV 1993] [JNV 1998] (1) 30 (2) 30.3 (3) 31 (4) 31.3 (1) 136 (2) 138 (3) 139 (4) 140  Answers 1. (1) 2. (4) 3. (2) 4. (4) 5. (1) 6. (2) 7. (3) 8. (2) 9. (3) 10. (3) 11. (2) 12. (1) 13. (3) 14. (4) 15. (4) 16. (3) 17. (1) 18. (2) 19. (4) 20. (1) 21. (2) 22. (2) 23. (4) 24. (1) 25. (1) 26. (2) 27. (4) Hints and Solutions 1. Sum of 20 observation = 20 × 65 = 1300 10. Q First five even numbers are = 2, 4, 6, 8, 10 after subtract 96 and add 69, we get 2 + 4 + 6 + 8 + 10 Their average = sum of correct 20 observation 5 = 1300 − 96 + 63 = 1273 30 = =6 Hence, mean of correct 20 observation 5 1273 3 + 5 + 7 + 8 + 9 32 = = 63.65 11. Average = = = 6.4 20 5 5 567 + 434 + 323 + 290 + 401 12. Average of 3 numbers = 10 2. Average = 5 ∴ Sum of 3 numbers = 10 × 3 = 30 2015 ∴ Average of first 2 numbers = 9 = = 403 5 ∴ Sum of first 2 numbers = 9 × 2 = 18 3. Now, total values = 20 × 18 = 360 ∴ Third number = 30 − 18 = 12 New total = 360 − 3 × 20 = 360 − 60 = 300 10 + 9 + 8 + 7 + 6 40 300 13. Average = = =8 ∴New average = = 15 5 5 20 14. Average of two numbers = 17 4. Q Average of 4 numbers = 7 ∴ Sum of two numbers = 17 × 2 = 34 ∴ Sum of 4 numbers = 4 × 7 = 28 One number = 21 Sum of first 3 numbers = 20 Then, other number = 34 − 21 = 13 Hence, fourth number = 28 − 20 = 8 15. Sum of the age of 5 boys = 15 × 5 = 75 yr 5. Required average 6 + 0 + 12 + 14 + 13 45 Other boy join, whose age = 75 + 15 = 90 yr = = =9 5 5 ∴ Average age of the whole group 90 6. Average height of the students = = 15 yr 30 + 40 + 50 + 60 + 70 250 6 = = = 50 5 5 16. Required average 7. Total score in first two matches = 2 × 27 = 54 140 + 135 + 142 + 138 + 140 695 = = 139 Total score in other 3 matches = 3 × 32 = 96 5 5 54 + 96 150 4 + 5 + 3.5 + 7.5 + 9.5 + 6.5 ∴ Average of 5 matches = = = 30 17. Average = 5 5 6 36 8. Sum of 20 values = 18 × 20 = 360 = =6 6 after subtract 3 from each, value, we get 18. Average of 3 numbers = 24 Sum of new 20 values = 360 − 3 × 20 ∴ Sum of 3 numbers = 24 × 3 = 72 = 360 − 60 = 300 300 ∴ Third number = 72 − ( 18 + 29) Therefore, new averagee = = 15 = 72 − 47 = 25 20 9. Total Ages of 3 children = 9 + 12 + 10 = 31 yr 19. Average income of family member 4000 + 3000 + 4400 11400 Total age of 4 children = 11 × 4 = 44 yr = = 3 3 ∴Age of 1 child = 44 − 31 = 13 yr =` 3800 84 Navodaya Vidyalaya (Class VI) Entrance Exam 20. Q Average score in 10 matches = 45.6 runs 5600 + 4500 ∴ Average expenditure = ∴Total score in 10 matches 12 = 45.6 × 10 = 456 runs 10100 2525 2 = = = ` 841 Q Average score in 6 matches = 48 runs 12 3 3 1 1 1 1 12 + 6 + 4 + 3 ∴Total score in 6 matches = 48 × 6 = 288 runs + + + ∴ Sum of the runs scored in last 4 matches 24. Average = 2 4 6 8 = 24 4 4 = 456 − 288 = 168 runs 25 ∴ Average score in last 4 matches = 24 = 25 = 25 = 0.26 168 4 24 × 4 96 = = 42 runs 4 8 + 6 + 0 + 9 + 7 30 25. Average = = =6 21. Sum of 5 consecutive even numbers starting 5 5 with 2 26. Total students in class I to V = 29 × 5 = 145 = 2 + 4 + 6 + 8 + 10 = 30 30 Total students in class I to III = 31 × 3 = 93 Average = =6 Total students in class IV to V = 145 − 93 = 52 5 5 + 5.2 + 6.3 + 7.2 + 6.3 ∴ Average of class IV and V = 52 = 26 22. Average length = 2 5 30 27. Average marks = =6 5 23 + 25 + 37 + 36 + 27 + 28 + 29  23. Total sum of 7 months expenditure  + 34 + 36 + 38 = = 7 × 800 = ` 5600 10 Total sum of 5 months expenditure 313 = = 313. = 5 × 900 = ` 4500 10 Practice Exercise 1. The average of all natural numbers from 7. The average age of 30 boys of a class is 521 and 525, is equal to 14 yr. When the age of the class (1) 525 (2) 251 (3) 526 (4) 523 teacher is included the average becomes 15 yr. The age of the class teacher is 2. The average of first 9 prime numbers is 2 1 (1) 40 yr (2) 42 yr (1) 9 (2) 11 (3) 11 (4) 11 (3) 48 yr (4) 45 yr 9 9 3. The average of first 6 even numbers is 8. The average marks of 4 men is increased (1) 7 (2) 6 (3) 8 (4) 5 by 3 when one of them whose marks are 120 is replaced by another man. What is 4. Find the average of first 10 natural the marks of new man? numbers. (1) 123 (2) 124 (1) 5 (2) 5.5 (3) 132 (4) 133 (3) 4.5 (4) 6 9. The average of 11 results is 30 that of the 5. Find the average of first 5 multiples of 3. first 5 is 25 and that of the last 5 is 28. The (1) 45 (2) 9 value of the 6th number is (3) 10 (4) 15 (1) 64 (2) 65 (3) 66 (4) 45 6. The average age of 25 boys in a class 10. Sachin Tendulkar in his 17th inning decreases by 6 months when a new boy makes a score of 85 and thereby increase takes the place of a 20 yr old boy. Find the his average by 3. What is his average after age of new boy. the 17th inning? (1) 7 yr (2) 7.5 yr (1) 37 (2) 35 (3) 33 (4) 39 (3) 8 yr (4) 8.5 yr Average 85 11. The average of 67 values is 35. If in each of 14. The body weight of 6 boys is recorded as these values 4 is added, the average of the 42 kg, 72 kg, 85 kg, 64 kg, 54 kg and new values will be 73 kg. What is the average body weight of (1) 37 (2) 39 all 6 boys? (3) 40 (4) 35 (1) 64 kg (2) 67 kg (3) 62 kg (4) 65 kg 12. The average of 25 observations was found 15. The average age of 5 officers in a to be 78.4. But later on it was detected department is 32 yr. If the age of their that 96 was misread as 69. The new supervisor is added the average increased correct average is by 1. What is the supervisor’s age? (1) 79.48 (1) 32 yr (2) 48 yr (3) 38 yr (4) 42 yr (2) 79 16. The average age of a brother and sister (3) 78.48 was 35 yr, 5 yr ago. What will be their (4) 80 average age (in yr) at present? 13. The average temperature from Monday to (1) 37.5 (2) 42 (3) 40 (4) 40.5 Thursday was 48°. The average 17. In a cricket team, the average age of temperature from Tuesday to Friday was 11 players and the coach is 18 yr. If the 52°. If temperature of Monday was 42°, age of the coach is not considered, the what is the temperature of Friday? average decreases by 1 yr. Find out the (1) 56° (2) 54° age of coach. (3) 58° (4) 60° (1) 27 yr (2) 28 yr (3) 29 yr (4) 31 yr Answers 1. (4) 2. (4) 3. (1) 4. (2) 5. (2) 6. (2) 7. (4) 8. (3) 9. (2) 10. (1) 11. (2) 12. (1) 13. (3) 14. (4) 15. (3) 16. (3) 17. (3) Hints and Solutions 1. Q Sum of all natural number from 521 to 525 Therfore, Average of first 10 natural number = 521 + 522 + 523 + 524 + 525 = 2615 55 = = 5.5 10 Therfore, average of all natural number from 2615 3 + 6 + 9 + 12 + 15 521 to 525 = = 523 5. Required average = 5 5 45 2. The average of first 9 prime number = =9 5 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 = 6. Total age decreased 9 100 1 = (Average age × Average decrement) = = 11 1 9 9 = 25 × = 12.5 2 3. Q Sum of first 6 even number = 2 + 4 + 6 + 8 + 10 + 12 = 42 Thus, age of new boy = 20 − 12.5 = 7.5 yr Therefore, average of first 6 even number 7. Total age of the boys of a class = 42 =7 = 14 × 30 = 420 yr 6 Total age when class teacher’s age is included 4. Q Sum of first 10 natural number = 15 × 31 = 465 yr = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 ∴ Age of class teacher = 465 − 420 = 45 yr 86 Navodaya Vidyalaya (Class VI) Entrance Exam 8. Marks of new man = 120 + 3 × 4 13. Average temperature from Monday to Thursday = 120 + 12 = 132 = 48° ∴ Total temperature = 48° × 4 = 192° 9. Total of 11 results = 11 × 30 = 330 Temperature of Monday = 42° Total of first 5 results = 25 × 5 = 125 ∴Temperature of Tuesday to Thursday Total of last 5 results = 28 × 5 = 140 = 192° − 42° = 150° 6th value = 330 − ( 125 + 140) Now, total temperature from Tuesday to Friday = 330 − 265 = 65 = 52° × 4 = 208° 10. Let the average of Sachin’s of the 16th inning be x. ∴ Temperature of Friday = 208° − 150° = 58° Then, the sum of 17 innings = 16x + 85 42 + 72 + 85 + 64 + 54 + 73 14. Average weight = and ( 16x + 85) = 17 ( x + 3) 6 ∴ x = 85 − 51 = 34 = 390 = 65 kg ∴ Average after 17 innings = 34 + 3 = 37 6 11. Total of 67 values = 67 × 35 = 2345 15. Total age of 5 officers = 32 × 5 = 160 Let the age of their supervisor be x. Then Value to be added in all = 4 × 67 = 268 160 + x = 6 × 33 ⇒ x = 198 − 160 = 38 yr ∴ Total value now = 2345 + 268 = 2613 2613 16. In present situation, their average age ∴ Average = = 39 = ( 35 + 5) = 40 yr 67 12. Previous total = 25 × 78.4 = 1960 17. Total age of 11 players + 1 coach = 12 × 18 = 216 yr ∴ New total = 1960 + 96 − 69 = 1987 Total age of 11 players = 11 × 17 = 187 yr 1987 ∴ New average = = 79.48 ∴ Age of coach = 216 − 187 = 29 yr 25  Self Practice 1. The average of 3 numbers is 9. If the average of first 2 numbers is 12, what is the third number? (1) 5 (2) 4 (3) 3 (4) 8 2. Average age of 5 boys is 13 yr. One more boy joins them and the average age becomes 12 yr. The age of the boy who joins last is (1) 12 yr (2) 13 yr (3) 14 yr (4) 7 yr 3. The average of three numbers is 12. The 2 numbers are 15 and 10, respectively. What is the third number? (1) 11 (2) 12 (3) 13 (4) 14 4. The rainfall of 4 cities is 52.96 cm, 62.56 cm, 53.91 cm and 35.93 cm, respectively. What is the average rainfall? (1) 50.25 cm (2) 60.05 cm (3) 55.80 cm (4) 51.34 cm 5. Rohit got marks in different subjects as 46, 55, 65, 34 and 40, respectively. What is the average of his marks? (1) 52 (2) 50 (3) 47 (4) 48 6. A cricket team scored 212, 170, 210, 260 and 398 runs respectively, in 5 cricket matches. What was the average number of runs in the 5 matches? (1) 250 (2) 240 (3) 245 (4) 260 7. The average of first 10 even numbers is (1) 5 (2) 12 (3) 10 (4) 11 8. The average of first 6 multiple of 15 is (1) 52.5 (2) 50 (3) 53.5 (4) 67.5 9. The average of the first 5 even numbers is (1) 4 (2) 5 (3) 6 (4) 7 10. The average of 4 numbers is 30. If the sum of first 3 numbers is 85, the fourth number is (1) 30 (2) 35 (3) 45 (4) 55 Answers 1. (3) 2. (4) 3. (1) 4. (4) 5. (4) 6. (1) 7. (4) 8. (1) 9. (3) 10. (2) CHAPTER 12 PERCENTAGE AND ITS APPLICATIONS Percentage Conversion of Per cent into Fraction Percentage means per hundred or for every 1 1 hundred. 1% = 20% = 100 5 Or 1 1 2% = 25% = The value which is considered for every hundred is 50 4 termed as percentage and the numerator of such 1 1 4% = 50% = fraction (having denominator 100) is called as the 25 2 rate of percentage. Percentage is represented by % 1 1 5% = 100% = sign. 20 1 1 10% = Basic Rules Related to Percentage 10 Per cent as a Fraction Finding a Percentage of a Number To convert a per cent into a fraction, we divide it by To find a per cent of a given number, we proceed as 100 and remove the per cent sign %. follows 5 1 ˜ Obtain the number, say x. e.g. 5% = = 100 20 ˜ Obtain the required per cent, say p%. 0.3 3 0.3 % = = ˜ Multiply x by p and divide by 100 to obtain the 100 1000 p 0.006 6 3 required p% of x. i.e. p % of x = ×x 0.006 % = = = 100 100 100000 50000 Fraction as a Per cent Important Formulae Result To convert a fraction into a per cent, we multiply it ¾ Rate percentage = × 100 Original number by 100 and apply the per cent sign %. 3 3 Increased percentage × 100  % = 75% ¾ e.g. = =  × 100 % Increment 4  4   Original number  0.4 = [ 0.4 × 100 ]% = 40 % ¾ Decreased percentage 0.08 = [ 0.08 × 100 ]% = 8 % =  × 100 % Decrement  Original number  Percentage and its Applications 89 Example 1. 25% is equal to Example 4. Kareena went to school for 216 days in a full (1) 1/2 (2) 1/4 (3) 1/8 (4) 1/16 year. If her attendance is 90%. Find the number of days 25 1 on which the school opened. Sol. (2) 25% = = 100 4 (1) 220 (2) 200 (3) 240 (4) 260 Sol. (3) Let the number of days on which the school Example 2. Find the value of x, if 3% of x is 9. opened is x. (1) 300 (2) 400 (3) 310 (4) 305 90 Now, 90% of x = 216 ⇒ × x = 216 Sol. (1) As, 3% of x is 9 100 3× x 9 × 100 216 × 100 ⇒ =9 ⇒ x= ⇒ x = 300 ⇒ x= 100 3 90 ⇒ x = 240 Example 3. Reena deposits 60 per month in her post Thus, the school opened for 240 days. office saving bank account. If this is 10% of her monthly income, find her monthly income. Example 5. 40% of (100 − 20% of 300) is equal to (1) ` 600 (2) ` 650 (3) ` 630 (4) ` 720 (1) 16 (2) 20 (3) 64 (4) 140 Sol. (1) 100 − 300 × Sol. (1) Let Reena’s monthly salary = ` x 20  40 40 × = (100 − 60) ×  100  100 100 Now, 10% of x = ` 60 40 × 40 10 60 × 100 = = 16 ⇒ × x = 60 ⇒ x = ⇒ x = ` 600 100 100 10 Entrance Corner 1. 150% is equal to [ JNV 2019] 7. 26.2% is equal to [ JNV 2016] (1) 1.5 (2) 5.1 (3) 0.15 (4) 15.0 (1) 2.62 (2) 0.262 (3) 0.0262 (4) 262.0 2. 84% is equal to [ JNV 2018] 17 8. can be expressed in percentage is 42 42 84 25 (1) (2) (3) (4) 8.4 [ JNV 2015] 100 50 225 (1) 34% (2) 68% (3) 17% (4) 25% 3. A student scored 18 marks out of 25 9. In a musical concert, 15% of the total marks in the first test of Math. In the is reserve for first class. If all the second test he scored 22 marks in the tickets were sold except 171 ticket of second test exceeds his first test by first class, then how many tickets were [ JNV 2017] sold? [ JNV 2014] (1) 4% (2) 8% (3) 16% (4) 80% (1) 1710 (2) 1600 (3) 1140 (4) 180 4. 90% of 300 + 30% of 90 is equal to 10. Which of the following is equivalent to 1.01? [ JNV 2014] [ JNV 2017] (1) 101% (2) 10.1% (3) 1.01% (4) 1010% (1) 287 (2) 297 (3) 237 (4) 277 11. Weight of tomato comprises 90% of 5. In an annual examination, Hardik got water. Weight of water in 25 kg of 500 marks out of 725. What is his tomato is [ JNV 2014] approximate per cent in the (1) 24 kg (2) 22.5 kg (3) 21 kg (4) 19.5 kg examination? [ JNV 2017] (1) 88 (2) 79 (3) 54 (4) 70 12. What is the percentage of 500 g of 4 kg? [ JNV 2013] 6. There are 3450 employees in an (1) 12.5 (2) 25 (3) 50 (4) 125 organisation. Out of which 42% got promoted. How many such employees 13. A man bought a bicycle for ` 1200. He are there who got promoted? [ JNV 2017] sold it for ` 1500. Find the profit (1) 1449 (2) 1518 per cent. [ JNV 2012] (3) 1587 (4) 1656 (1) 30 (2) 20 (3) 25 (4) 28 90 Navodaya Vidyalaya (Class VI) Entrance Exam 14. A boy gets ` 20 per month and spends 23. 0.075 when expressed as per cent, is 50% of it. How much does he save in [ JNV 2002] 1 yr? [ JNV 2012] (1) 75% (2) 7.5% (3) 0.75% (4) 0.075% (1) ` 100 (2) ` 50 24. Out of a total of 250 marks, a student (3) ` 120 (4) ` 40 got 30% marks and failed by 25 marks. 15. Rajesh purchased a watch for ` 300. He The marks necessary for passing is sold it for ` 330. Find the profit per cent. [ JNV 2001] [ JNV 2012] (1) 50 (2) 75 (3) 100 (4) 125 (1) 5 (2) 13 (3) 14 (4) 10 25. 30% of ` 40 is equal to [ JNV 2000] 16. The original price of a car is ` 500000. (1) ` 10 (2) ` 11 (3) ` 12 (4) ` 13 What is the new price if the original 5 price is reduced by 10%? [ JNV 2012] 26. may be expressed as 8 [ JNV 2000] (1) ` 540000 (2) ` 460000 50 (1) % (2) 62.5% (3) 55.5% (4) 70.5% (3) ` 450000 (4) ` 480000 80 17. Which one of the following is equivalent 27. 20% of ` 70 is equal to [ JNV 2000] of 6/20? [ JNV 2011] (1) ` 14 (2) ` 15 (3) ` 16 (4) ` 17 (1) 6% (2) 20% 28. 25% of 10 m is [ JNV 2000] (3) 26% (4) 30% (1) 50 cm (2) 100 cm (3) 200 cm (4) 250 cm 18. Out of 600 students 240 are girls. What 29. A person spends 50% of his salary and is the percentage of girls? [ JNV 2011] saves ` 200 per month. His monthly (1) 250 (2) 60 (3) 40 (4) 24 salary is [ JNV 1999] 19. The population of a district is 20 lakh. It (1) ` 300 (2) ` 400 (3) ` 500 (4) ` 600 increases by 1.1% every year. What is 30. 50% is equal to [ JNV 1998] the population after 1 yr? [ JNV 2010] 1 1 1 1 (1) 21.1 lakh (2) 22 lakh (1) (2) (3) (4) 2 3 4 5 (3) 22.2 lakh (4) 20.22 lakh 31. The catalogue price of an article is ` 200. 20. 200 students appeared in an A reduction of 15% in made for each examination. If 75% of student passed purchase. The cash price is [ JNV 1998] the examination, find the number of (1) ` 150 (2) ` 170 (3) ` 180 (4) ` 200 students who passed the examination. [ JNV 2008] 32. 20% of ` 10 is [ JNV 1997] (1) 150 (2) 100 (3) 275 (4) 175 (1) ` 2 (2) ` 1 (3) ` 3 (4) ` 4 21. In per cent, what is 10.01 written as? 33. Find the sum whose 20% is ` 240. [ JNV 2005] [ JNV 1997] (1) 10.01% (2) 10% (1) ` 1200 (2) ` 1000 (3) ` 6000 (4) ` 2000 (3) 1001% (4) 100100% 34. John had ` 300. He spent ` 100 on 22. 80% of ` 240 is more than 35% of books. Find his per cent expenditure. ` 400 by [ JNV 2004] [ JNV 1997] (1) ` 52 (2) ` 42 (3) ` 192 (4) ` 140 1 2 (1) 20 (2) 30 (3) 33 (4) 16 3 3 Answers 1. (1) 2. (2) 3. (3) 4. (2) 5. (4) 6. (1) 7. (2) 8. (2) 9. (3) 10. (1) 11. (2) 12. (1) 13. (3) 14. (3) 15. (4) 16. (3) 17. (4) 18. (3) 19. (4) 20. (1) 21. (3) 22. (1) 23. (2) 24. (3) 25. (3) 26. (2) 27. (1) 28. (4) 29. (2) 30. (1) 31. (2) 32. (1) 33. (1) 34. (3)  Hints and Solutions 1. Given, 150% 330 − 300 15. Required profit per cent = × 100 150 15 300 150% is written as = = 15. 30 100 10 = × 100 = 10% 84 42 300 2. 84% = = ( 100 − 10) 100 50 16. New price of the car = 500000 × 3. More marks = 22 − 18 = 4 100 90 4 × 100 = 500000 × = ` 450000 Required percentage = = 16% 100 25 6 6 100 4. 90% of 300 + 30% of 90 17. in percentage = × = 30% 20 20 1 90 × 300 30 × 90 240 = + 18. Percentage of girls = × 100 = 40% 100 100 600 = 90 × 3 + 3 × 9 = 270 + 27 = 297 19. District population after one year 500 = 2000000 + 2000000 × 11.% 5. Required percentage = × 100 = 68.9 ≈ 70 725 11. = 2000000 + 2000000 × 42 144900 100 6. 3450 × = = 1449 got promotion 100 100 = 2000000 + 22000 26.2 = 2022000 7. 26.2% = = 0.262 100 75 20. Required number = 200 × = 150 17 17 100 8. Percentage value of = × 100 = 68% 1001 25 25 21. 10.01 = = 1001% 9. According to the question, 100 240 × 80 15% = 171 22. 80% of ` 240 = = ` 192 100 171 1% = 400 × 35 15 35% of ` 400 = = ` 140 100 171 × 100 ∴ 100% = = 1140 ∴ Difference = (192 – 140) = ` 52 15 Hence, total number of ticket sold = 1140 23. 0.075 = 0.075 × 100 = 7.5% (To express 101 number into per cent it is multiplied by 100) 10.. = 101 = 101% 100 24. Q Total marks = 250 11. Weight of water in 25 kg of tomato = 90% of 25 kg Student got = 30% = 22.5 kg 30 i.e., 250 × = 75 marks 100 12. Q 1 kg = 1000 g Failed by = 25 marks ∴ 4 kg = 4 × 1000 g = 4000 g ∴ Pass marks = 75 + 25 = 100 500 Hence, required percentage = × 100 25. Q Out of 100 = 30 4000 30 = 12.5% ∴ Out of 1 = 100 13. Given, cost price of the bicycle = ` 1200 30 ∴Out of 40 = × 40 = ` 12 and selling price of the bicycle = ` 1500 100 Hence, required profit percentage 5 5 500 26. = × 100% = % = 62.5% 1500 − 1200 300 8 8 8 = × 100 = × 100 = 25% 20 1200 1200 27. 20% of ` 70 = × 70 = ` 14 100 14. Monthly saving amount by the boy 50 28. 25% of 10 m = 25% of 1000 cm = 20 × = ` 10 25 100 = × 1000 = 250 cm 100 ∴Annually saving amount = 10 × 12 = ` 120 92 Navodaya Vidyalaya (Class VI) Entrance Exam 29. Savings = 100% − 50% = 50% = ` 200 33. Let the sum be ` x. 100 Then, 20% of x = ` 240 ∴Total salary = × 200 = ` 400 50 20 ⇒ x × = 240 50 1 100 30. 50% = = 100 2 240 × 100 ∴ x = = ` 1200 31. Reduction at 15% on ` 200 20 15 34. Q Out of ` 300 expenditure = ` 100 = × 200 = ` 30 100 100 ∴Cash price = Catalogue price − Reduction ∴ Out of ` 1 expenditure = ` 300 = 200 − 30 = ` 170 100 1 ∴` 100 expenditure = × 100 = 33 % 20 300 3 32. 20% of ` 10 = × 10 = ` 2 100 Practice Exercise 1. Which one of the following is equal to 10. 12% of 12 + 12 is equal to 6.25%? (1) 12.36 (2) 12.44 (3) 13.44 (4) 26.40 (1) 0.00625 (2) 0.0625 11. If 5% of X + 16% of 75 = 16. Find the (3) 0.625 (4) 6.25 value of X. 2. 40% of 20% is equal to (1) 75 (2) 80 (3) 90 (4) 100 (1) 16% (2) 20% (3) 8% (4) 80% 12. After spending 30% of her money, a lady 3. Express 45% in fraction. has ` 70 left. How much had she first? 9 9 (1) (2) (1) ` 80 (2) ` 100 20 10 3 5 (3) ` 120 (4) ` 140 (3) (4) 20 20 13. Ram’s monthly salary was ` 3000. Find 1 his salary now after an increase of 20%. 4. Express 10 into percentage. 10 (1) ` 2400 (2) ` 3200 (1) 1010% (2) 10.10% (3) ` 3400 (4) ` 3600 (3) 0.101% (4) 101% 14. In a class of 50 students, 40% are girls. 5. 50 is what per cent of 75? How many boys are there? 100 50 (1) % (2) % (1) 20 (2) 10 (3) 25 (4) 30 3 3 200 15. Out of 30 students 40% are boys and (3) % (4) None of these 3 the remaining are girls. The number of 6. 25 g is what per cent of 1 kg? girls in the class (1) 25% (2) 2.5% (1) 12 (2) 15 (3) 18 (4) 20 (3) 0.25% (4) 0.025% 16. A person earns ` 1800 per month and 7. 25% of 75 is equal to saves 10% of it. How much does he (1) 16 (2) 16.35 (3) 17.45 (4) 18.75 save? (1) ` 180 (2) ` 1620 8. How many per cent of 72 is 18? 1 (3) ` 1790 (4) ` 1810 (1) 25% (2) 33 % 3 17. A person saves 25% of his income. If he (3) 42% (4) 50% saves ` 3000 per month, his monthly 9. (100% of 5) + (5% of 100) is equal to income is (1) 10 (2) 15 (1) ` 15000 (2) ` 12000 (3) 55 (4) 105 (3) ` 9000 (4) ` 7500 Percentage and its Applications 93 18. In March, 1994 the price of a car was 22. It is known that 6% of the mangoes are ` 67000. In April, 1994 its price was rotten. If the number of rotten mangoes raised by 10%. The price of the car in is 54, then the total number of April, 1994 was mangoes is (1) ` 60300 (2) ` 66330 (1) 900 (2) 950 (3) ` 67670 (4) ` 73700 (3) 1010 (4) 1040 19. If the population of a city recorded in 23. A total of 20000 votes were polled in an year 2001 and 2011, 560400 and election contested by two candidates. 700500 respectively, then the per cent The winning candidate got 60% of the increase in the population is total votes polled. How many votes did (1) 20 (2) 30 (3) 35 (4) 25 the defeated candidate got? 20. The total number of students in a school (1) 800 (2) 1200 (3) 8000 (4) 12000 is 5600 out of which 60% are boys, what is the total number of girls in this 24. A boy gets 25 marks out of 80 and fails school? by 15 marks. Find the percentage of (1) 2240 (2) 3360 pass marks. (3) 2860 (4) None of these (1) 40 (2) 30 (3) 33 (4) 50 21. If a man after spending 85% of the 25. A student has to secure 40% marks to income he saves ` 4560 per month, his pass. If he gets 20 marks and fails by monthly income is 20 marks, the maximum marks are (1) ` 32800 (2) ` 31600 (1) 20 (2) 40 (3) ` 30400 (4) None of these (3) 80 (4) 100 Answers 1. (2) 2. (3) 3. (1) 4. (1) 5. (3) 6. (2) 7. (4) 8. (1) 9. (1) 10. (3) 11. (2) 12. (2) 13. (4) 14. (4) 15. (3) 16. (1) 17. (2) 18. (4) 19. (4) 20. (1) 21. (3) 22. (1) 23. (3) 24. (4) 25. (4) Hints and Solutions 6.25 625 25 75 1. 6.25% = = = 0.0625 7. 25% of 75 = × 75 = = 18.75 100 10000 100 4 20 40 18 2. 20% = and 40% = 8. Required percentage = × 100 = 25% 100 100 72 40 20 8 ∴ 40% of 20% = × = or 8% 9. (100% of 5) + (5% of 100) 100 100 100 =  × 5 +  × 100 = 5 + 5 = 10 100 5 45 9  100   100  3. 45% = = 100 20 12 1 101 101 10. 12% of 12 + 12 = × 12 + 12 4. 10 = = × 100 = 1010% 100 10 10 10 = 1.44 + 12 = 13.44 50 200 5. Required percentage = × 100 = % 11. Q 5% of X + 16% of 75 = 16 75 3 25 g 16 6. Required percentage = × 100 ∴ 5% of X + × 75 = 16 1 kg 100 25 g ⇒ 5% of X + 12 = 16 = × 100 = 2.5% ⇒ 5% of X = 16 − 12 = 4 1000 g 5 4 × 100 ⇒ × X =4 ⇒ X = = 80 100 5 94 Navodaya Vidyalaya (Class VI) Entrance Exam 700500 − 560400  12. Let the total amount be ` x. 19. Required per cent =  × 100 Then, x − 30% of x = ` 70  560400  30x = × 100 = 25% ⇒ x − = 70 140100 100 560400  100x − 30x ⇒ = 70 ⇒ 70x = 70 × 100 20. Number of boys = 60% of 5600 100 70 × 100 60 ∴ x = = `100 = × 5600 = 3360 70 100 Hence, number of girls = 5600 − 3360 = 2240 13. ∴Required salary = 3000 + 20% of 3000 21. Savings of the man = ( 100 − 85)% = 15% 20 = 3000 + 3000 × Let the monthly income = ` x 100 = 3000 + 600 = ` 3600 Then, 15% of x = 4560 15 14. Total students = 50 ⇒ × x = 4560 100 Percentage of girl = 40% 4560 × 100 Number of boys = 50 × 60% ∴ x = = ` 30400 15 50 × 60 Hence, monthly income of man = ` 30400 = = 30 100 22. Let the total number of mangoes = x 15. Total students = 30 Then, 6% of x = 54 Q Percentage of boys = 40% 6 54 ⇒ × x = 54 ⇒ x = × 100 = 900 ∴ Percentage of girls = 100 − 40 = 60% 100 6 60 30 Hence, total number of mangoes = 900 ∴Number of girls = × = 18 100 1 23. Total votes polled = 20000 1800 × 10 16. His saving = = ` 180 The winning candidate got 60% of the total 100 17. Let the monthly income of man is ` x. votes polled. 20000 × 60 ∴ x × 25 = 3000 ∴ = 12000 votes 100 100 3000 × 100 ∴ The defeated candidate got ∴ x = = 20000 − 12000 = 8000 votes 25 = ` 12000 24. Pass marks = 25 + 15 = 40 40 18. 10% of 67000 = 10 × 67000 = ` 6700 Percentage of pass marks = × 100 = 50% 100 80 ∴ Price of the car in April, 1994 25. Marks required to pass = 40% = 20 + 20 = ( 67000 + 6700) 100 × 40 ∴ Maximum marks = = 100 = ` 73700 40  Self Practice 2 1. Which one of the following is equivalent to 16 %? 3 50 1 16 2 (1) (2) (3) (4) 3 6 3 3 2. Which one of the following equivalent to 28%? (1) 2.8 (2) 0.28 (3) 28 (4) 280 1 3. Convert 1 into a percentage. 4 (1) 80% (2) 125% (3) 1.25% (4) 12.5% 4. What percentage is 40 paise of ` 2.50? (1) 16% (2) 100% (3) 10% (4) 8% 5. If 36% of pupils in a school are girls and the number of boys in the school is 816, how many girls are there in the school? (1) 459 (2) 357 (3) 457 (4) 359 6. A man get a 10% increase in his salary. His new salary is ` 10285, what was his original salary? (1) ` 11313 (2) ` 9350 (3) ` 8350 (4) ` 10350 7. A football team won 40% of the total number of matches it played during a year. If it lost 6 matches in all and no match was drawn, find the total number of matches played by the team during the year. (1) 20 (2) 8 (3) 12 (4) 10 8. Chalk contains 10% calcium, 3% carbon and 12% oxygen. The amount of each of these in 1 kg of chalk are (1) 30 g, 20 g, 10 g (2) 30 g, 100 g, 120 g (3) 100 g, 30 g, 120 g (4) 120 g, 30 g, 100 g 9. 1/8 is equal to 1 (1) 25% (2) 16% (3) 12 % (4) 0.12% 2 10. 600% can be expressed in decimal as (1) 60.0 (2) 6.0 (3) 6000 (4) 3/5 11. Sachin got 60% marks in Maths and 3 marks less than Maths in Science. If the total marks are 150, how many marks he scored in Science? (1) 90 (2) 95 (3) 87 (4) 63 12. 20% of 60 is equal to (1) 12 (2) 1200 (3) 3 (4) 30 13. What per cent of 90 is 27? (1) 30% (2) 10% (3) 9% (4) 3% 14. What rate per cent is 1 min 12 s to 1h? (1) 2% (2) 3% (3) 4% (4) 5% 15. A person spends 75% of his salary and saves ` 150 per month. His monthly salary is (1) ` 750 (2) ` 600 (3) ` 400 (4) ` 300 Answers 1. (2) 2. (2) 3. (2) 4. (1) 5. (1) 6. (2) 7. (4) 8. (3) 9. (3) 10. (2) 11. (3) 12. (1) 13. (1) 14. (1) 15. (2)