Math Concepts and Problems for Class 10

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Questions and Answers

What is the new number added if the average of 25 numbers is 90 and increases to 95 after adding the new number?

  • 300
  • 240
  • 280 (correct)
  • 220

What percent of the total patients admitted in all three hospitals in May does the total patients admitted in A in March represent?

  • 30%
  • 15%
  • 20% (correct)
  • 25%

What is the difference between the total male patients admitted in A in April and in B in March together and the total patients admitted in C in May?

  • 1419
  • 1469 (correct)
  • 1369
  • 1459

If total male patients admitted in C in June are 20% more than those admitted in March, how many female patients were admitted in C in June?

<p>1100 (B)</p> Signup and view all the answers

What is the ratio of total patients admitted in A in April to patients admitted in all three hospitals in May?

<p>28:73 (D)</p> Signup and view all the answers

How does the total patients admitted in A in May compare percentwise to the total patients admitted in B & C in April?

<p>65% (B)</p> Signup and view all the answers

Identify the wrong number in the series: 27, 48, 80, 134, 221, 355, 538.

<p>355 (C)</p> Signup and view all the answers

Which number is incorrect in the series: 215, 200, 250, 175, 275, 150, 300?

<p>300 (A)</p> Signup and view all the answers

What is the value of the question mark (?) in the equation 60% of 700 - 450 = ? - 85% of 120?

<p>64 (B)</p> Signup and view all the answers

What is the value of the question mark (?) in the equation 36% of 250 + 26 + 2 * ? = 207?

<p>8 (C)</p> Signup and view all the answers

What will come in the place of the question mark (?) in the equation 240 x 2.5 + 65 x 2/13 = ?² - √225?

<p>24 (A)</p> Signup and view all the answers

How many days will it take to complete the work if A works alone for four days before B joins?

<p>12 days (C)</p> Signup and view all the answers

What is the value of the question mark (?) in the equation 4080 ÷ (? + 17) = 102 + 2?

<p>23 (C)</p> Signup and view all the answers

After how many months did Q join P in the business if their profit share became equal after one year?

<p>4 months (D)</p> Signup and view all the answers

What will be the value of the question mark (?) in the equation 945 ÷ 35 x 20 = ?

<p>560 (A)</p> Signup and view all the answers

What will come in the place of the question mark (?) in the equation (132 + 72) ÷ 12 x 17 = ? + 9²?

<p>287 (D)</p> Signup and view all the answers

What is the cost price of the article if the marked price is Rs. 800, with a discount of 10% and a profit of 20%?

<p>Rs. 640 (B)</p> Signup and view all the answers

What is the value of the question mark (?) in the equation 5 * 30 ÷ √144 x 20 = ?

<p>208 (C)</p> Signup and view all the answers

How many total students are there in the school if 360 students passed and 66.66% of boys who passed equals 160?

<p>720 (B)</p> Signup and view all the answers

What will come in the place of the question mark (?) in the equation 0.26 x 50 + 132 = ?

<p>180 (A)</p> Signup and view all the answers

What is the largest of three consecutive numbers whose squares sum up to 1085?

<p>20 (C)</p> Signup and view all the answers

What is the speed of the stream if the boat's speed in still water is 12 km/h and the time taken downstream equals the time taken upstream?

<p>4 km/h (A)</p> Signup and view all the answers

What is the present age of A if it is 14 years more than B and their age ratio was 2:1 twelve years ago?

<p>32 years (C)</p> Signup and view all the answers

What is the value of the second discount percentage x if the selling price after two discounts is Rs. 1470?

<p>24% (A)</p> Signup and view all the answers

Flashcards

Work rate of A & B

A can complete a work in 24 days, and B in 18 days. Finding the combined work rate if they work together.

Equal profit sharing

P invested Rs. 21000 and Q, invested Rs. 28000 in a business. Profit is shared equally at the end of the year. Find the time Q joined the business.

Cost price with discount and profit

Marked price Rs. 800, discount 10%, profit 20%. Determine the cost price of the article.

Percentage of passed students

360 students passed. Find total students if 66.66% of passed boys is 160 and 60% of boys passed and 40% of girls passed.

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Consecutive squares

Find the largest number if the sum of squares of three consecutive numbers is 1085.

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Ratio of marks

Ria, Ram, and Pooja got 74 marks together. Ria:Pooja = 4:5, Pooja:Ram = 3:2. Find Ram's marks.

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Speed of boat stream

Boat speed in still water is 12 km/hr. Downstream time = Upstream time to cover 20 km and 10 km. Find stream speed.

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Age problem

A is 14 years older than B. Ratio of A's age to B's age 12 years ago was 2:1. Find A's age.

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Successive Discounts

Marked price of Rs. 2450, successive discounts of 20% and x%, selling price is Rs. 1470. Find x.

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Difference in Simple Interest

A and B invested the same amount for 5 years at 12% and 18% simple interest respectively. Interest difference is Rs. 1440. Find the total investment.

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Average of 25 numbers

Sum of 25 numbers divided by 25

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Increased average by 5

New average is 5 more than original average

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Percentage calculation

A part of a whole expressed as a fraction of 100

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Total patients admitted

Sum of all patients admitted in a specific group (hospital/month)

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Patient Ratio calculation

Comparison between patients in one hospital/group against another hospital/group

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Number series

Sequence of numbers following a certain pattern

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Wrong Number in Series

Find the number in a series that is not part of the pattern

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25 numbers average increased by 5

Calculation to derive the unknown number added to the list to increase the average by five

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Percentage of total patients admitted in March

Proportion of patients admitted in a specific hospital in a certain month compared to the total admitted in all hospitals in the same month

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Difference between total male patients

Find the difference between the male patients in two particular hospital and groups

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Male/Female patients admitted in June

Calculation of total male patients for a group (hospital) in a certain month based on the corresponding group/month data

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Ratio of total patients

Comparison of total patients admitted in one hospital in a particular month versus total patients across multiple hospitals in a specific month

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Percentage of patients in May

Calculation to find the percentage of patients admitted in one particular hospital for a month compared to the summation of patients admitted in multiple hospitals in another month (usually different in time)

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√256

The square root of 256

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25% of 256

One-quarter of a 256.

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274 - 141

Subtracting 141 from 274

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36% of 250

36/100 * 250.

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240 x 2.5

240 multiplied by 2.5

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65 x 2/13

65 multiplied by two-thirteenth

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√225

The square root of 225

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4080 ÷ (x + 17)

Dividing 4080 by the sum of x and 17

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31.5 - 3.5 x 12

31.5 minus product of 3.5 and 12

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945 ÷ 35

Dividing 945 by 35

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60% of 700

60% of the number 700

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30 ÷ (x)

30 divided by x

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√144

Square root of 144

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85% of 120

85 per cent of 120

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(0.9)^2

0.9 raised to the power of 2

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132 + 72

Sum of 132 & 72

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132 ÷ 12

Dividing 132 by 12

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26% of 50

26/100 * 50

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10 + 2.9

Sum of 10 & 2.9

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(132 + 72) ÷ 12

Sum of 132 and 72 divided by 12

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9²

9 multiplied by 9

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0.26 x 50

Decimal multiplied by a whole number

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Study Notes

Question 31

  • A can complete a task in 24 days.
  • B can complete the same task in 18 days.
  • A starts working alone for 4 days.
  • B joins A after 4 days.
  • Total time to complete task: 12 days.

Question 32

  • P invests Rs. 21000.
  • Q joins the business after a few months with Rs. 28000.
  • Profit share of P and Q is equal at the end of one year.
  • Q joined the business after 4 months.

Question 33

  • Marked price of an item: Rs. 800.
  • Discount given: 10%.
  • Shopkeeper gains 20%.
  • Cost price of the item: Rs. 720.

Question 34

  • Total students who passed the exam: 360.
  • 60% of total boys passed.
  • 40% of total girls passed.
  • 66 2/3% of passed boys = 160
  • Total students in the school: 960.

Question 35

  • Sum of squares of three consecutive numbers: 1085.
  • Largest number: 21.

Question 36

  • Ria, Ram, and Pooja got a total of 74 marks.
  • Ratio of Ria's marks to Pooja's marks: 4:5.
  • Ratio of Pooja's marks to Ram's marks: 3:2.
  • Total marks scored by Ram: 20.

Question 37

  • Speed of boat in still water: 12 km/hour.
  • Time taken to cover 20 km downstream = time taken to cover 10 km upstream.
  • Speed of the stream: 4 km/hour.

Question 38

  • Present age of A is 14 years more than B.
  • 12 years ago, ratio of A's age to B's age was 2:1.
  • Present age of A: 32 years.

Question 39

  • Marked price of an article: Rs. 2450.
  • Successive discounts of 20% and x%.
  • Selling price of the article: Rs. 1470.
  • Value of x: 15%.

Question 40

  • A and B invested equal amounts.
  • A invested at 12% p.a.
  • B invested at 18% p.a.
  • Difference in interests received by A and B: Rs. 1440.
  • Total amount invested by A and B together: Rs. 9600.

Question 41

  • Average of 25 numbers: 90.
  • Average increases by 5 after adding a new number.
  • New number: 300.

Question 42

  • Total patients admitted in A in March: 1505.
  • Total patients admitted in all three hospitals in May: 2864 + 2228 + 2408 = 7480
  • Percentage of total patients admitted in A in March: 20%.

Question 43

  • th of total patients admitted in B in March are female: 1/4.
  • 60% of total patients admitted in A in April are female.
  • Difference = (Total male patients admitted in A in April + Total male patients admitted in B in March) - (Total patients admitted in C in May)

Question 44

  • 956 of total patients admitted in C in March are female.
  • Total male patients admitted in C in June are 20% more than total male patients admitted in C in March.
  • Total patients admitted in June in C is 872 more than total patients admitted in B in May
  • Total female patients admitted in C in June: 1300.

Question 45

  • Ratio of (Total patients admitted in A in April) and (Total patients admitted in all hospitals in May): 14:37.

Question 46

  • Total patients admitted in A in May: 2864
  • Total patients admitted in B & C in April: 1976+2228+2804 = 6918
  • Percentage: 41%.

Question 47

  • Wrong number in the series 27, 48, 80, 134, 221, 355, 538 : 355,

Question 48

  • Wrong number in the series 215, 200, 250, 175, 275, 150, 300 : 150

Question 49

  • Wrong number in the series 550, 4400, 110, 440, 24, 44, 4.4 : 4400

Question 50

  • Wrong number in the series 146, 145, 149, 122, 138, 15, 49 : 15

Question 51

  • Wrong number in the series 1.7, 3.0, 5.6, 9.5, 14.7, 21.8, 29 : 29

Question 52

  • Calculation to fill in question mark in √256 25% of 256 +
    × 8 = ? + 10 . Answer:64 4

Question 53

  • Calculation to fill in question mark in 274-141= ? +98 . Answer:31

Question 54

  • Calculation to fill in question mark in 36% of 250 +26+2×?=207 . Answer:8

Question 55

  • Calculation to fill in question mark in 2^240 x 2.5 + 65 = ?^2 - √225 . Answer: 27

Question 56

  • Calculation to fill in question mark in 4080÷(?+17)=102+2 . Answer:23

Question 57

  • Calculation to fill in question mark in 31.5 × 3.5 × 12 – 8 = ?^2 . Answer:35

Question 58

  • Calculation to fill in question mark in 945 ÷ 35 x 20 = ? . Answer:540

Question 59

  • Calculation to fill in question mark in 60% of 700-450-85% of 120 = ? . Answer:64

Question 60

  • Calculation to fill in question mark in 30 ÷ 5/12 + √144 x 20 = ? . Answer: 380

Question 61

  • Calculation to fill in question mark in 4/1 2 16 = (27 + 45/35 + 3) /21= ? . Answer: 5

Question 62

  • Calculation to fill in question mark in (0.9)^2 x 10 +2.9 = ? + 132/12 . Answer :2

Question 63

  • Calculation to fill in question mark in 26 % of 50 ×5 ÷ 26 = ? . Answer: 2.5

Question 64

  • Calculation to fill in question mark in (132+72) ÷12 x 17 = ? + 92 . Answer: 168

Question 65

  • Calculation to fill in question mark in 0.26 x 50 + 132 = ?. Answer: 182

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