CBSE Class 10 Mathematics Percentage MCQs Set 09

Multiple Choice Questions (MCQs) for Class 10 Mathematics: Percentage

Explore reliable objective questions for Percentage tailored for Class 10 learners. Utilizing these Mathematics multiple-choice formats ensures thorough preparation and strengthens problem-solving speed for upcoming school assessments.

Practice Percentage MCQs for Class 10 Mathematics

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Multiple Choice Questions

Question 1: The number of enrolments in a school increased from 1800 to 2016. The percentage increase in the enrolments is
(a) 10%
(b) 11%
(c) 12%
(d) 13%
Show Answer & Explanation

Answer: (c) 12%

Explanation:
1. Increase = 2016 − 1800 = 216
2. Percentage increase = 216/1800 × 100 = 12%.

Teacher's Note:
1. Percentage change = (change / original) × 100.
2. The original value is always the base.

Question 2: The price of a commodity is increased by 40%. By what percent should a consumer reduce his consumption so that his expenditure on the commodity remains constant?
(a) 25 4/7%
(b) 26 4/7%
(c) 27 4/7%
(d) 28 4/7%
Show Answer & Explanation

Answer: (d) 28 4/7%

Explanation:
1. Let the price be 100 and the consumption 1; new price = 140
2. Consumption must become 100/140 = 5/7, a reduction of 2/7 = 28 4/7%.

Teacher's Note:
1. Expenditure = price × consumption.
2. Reduction = increase / (100 + increase) × 100.

Question 3: If Ram's salary went up by 25%, then by what percent should it be brought down to bring it to its initial value?
(a) 25%
(b) 20%
(c) 33.33%
(d) 37.5%
Show Answer & Explanation

Answer: (b) 20%

Explanation:
1. Let the salary be 100; new = 125
2. Reduction needed = 25/125 × 100 = 20%.

Teacher's Note:
1. The base for the fall is the new, larger value.
2. So the fall is smaller than the rise.

Question 4: A number, when decreased by 20%, becomes 136. What is the number?
(a) 160
(b) 150
(c) 170
(d) 140
Show Answer & Explanation

Answer: (c) 170

Explanation:
1. 80% of the number = 136
2. Number = 136 × 100/80 = 170.

Teacher's Note:
1. Write the decrease as a percentage of the original.
2. Divide by 0.8.

Question 5: If 60% of K is 30 less than 75% of K, then what is the value of K?
(a) 500
(b) 300
(c) 400
(d) 200
Show Answer & Explanation

Answer: (d) 200

Explanation:
1. 75% of K − 60% of K = 30
2. 15% of K = 30, so K = 200.

Teacher's Note:
1. Translate the words into an equation.
2. 15/100 × K = 30.

Question 6: The length of a rectangle is increased by 10% while its breadth is decreased by 10%. What is the consequent percentage change in the area of the rectangle?
(a) 1% increase
(b) 10% increase
(c) 10% decrease
(d) 1% decrease
Show Answer & Explanation

Answer: (d) 1% decrease

Explanation:
1. New area = 1.1 × 0.9 = 0.99 of the old area
2. The area decreases by 1%.

Teacher's Note:
1. Multiply the two factors, not the percentages.
2. (+a)(−a) gives a net change of −a²/100 %.

Question 7: In an examination, Ramu and Raju secured 783 and 684 marks respectively. If Ramu secured 87% marks, then the percentage of marks secured by Raju is
(a) 75%
(b) 76%
(c) 77%
(d) 78%
Show Answer & Explanation

Answer: (b) 76%

Explanation:
1. Total marks = 783 × 100/87 = 900
2. Raju's percentage = 684/900 × 100 = 76%.

Teacher's Note:
1. First find the maximum marks from Ramu's data.
2. Then apply it to Raju.

Question 8: In an examination, Ramesh secured 574 marks and Rekha secured 76% of the total marks. If Ramesh secured 82% of the total marks, the difference in their marks is
(a) 40
(b) 41
(c) 42
(d) 43
Show Answer & Explanation

Answer: (c) 42

Explanation:
1. Total = 574 × 100/82 = 700
2. Rekha's marks = 76% of 700 = 532
3. Difference = 574 − 532 = 42.

Teacher's Note:
1. Find the total from Ramesh's score.
2. Then compute Rekha's marks.

Question 9: By what percent will the area of a square change if its side is increased by 10%?
(a) 10% increase
(b) 20% increase
(c) 10% decrease
(d) 21% increase
Show Answer & Explanation

Answer: (d) 21% increase

Explanation:
1. New area = (1.1)² = 1.21 times the old area
2. The area increases by 21%.

Teacher's Note:
1. Area depends on the square of the side.
2. Use (1 + r)² for a rate r.

Question 10: The population of a city increases by 30% every year. If the present population is 338000, then what was the population of the city two years ago?
(a) 300000
(b) 250000
(c) 200000
(d) 240000
Show Answer & Explanation

Answer: (c) 200000

Explanation:
1. Present = P × 1.3² = 1.69P
2. P = 338000/1.69 = 200000.

Teacher's Note:
1. Compound growth multiplies by 1.3 each year.
2. Divide to go back in time.

Question 11: 860% of 50 + 50% of 860 =
(a) 430
(b) 516
(c) 860
(d) 960
Show Answer & Explanation

Answer: (c) 860

Explanation:
1. 860% of 50 = 430
2. 50% of 860 = 430
3. Sum = 860.

Teacher's Note:
1. x% of y = y% of x.
2. Both terms are equal here.

Question 12: 60% of 264 is the same as
(a) 10% of 44
(b) 15% of 1056
(c) 30% of 132
(d) None of these
Show Answer & Explanation

Answer: (b) 15% of 1056

Explanation:
1. 60% of 264 = 158.4
2. 15% of 1056 = 158.4, while the others give 4.4 and 39.6.

Teacher's Note:
1. Compute the value of the given quantity first.
2. Then test each option.

Question 13: How many litres of pure acid are there in 8 litres of a 20% solution?
(a) 1.4
(b) 1.5
(c) 1.6
(d) 2.4
Show Answer & Explanation

Answer: (c) 1.6

Explanation:
1. Acid = 20% of 8 = 1.6 litres.

Teacher's Note:
1. Percentage of a quantity = (percentage/100) × quantity.
2. The remaining 6.4 litres is water.

Question 14: What is 25% of 25% equal to?
(a) 0.00625
(b) 0.0625
(c) 0.625
(d) 6.25
Show Answer & Explanation

Answer: (b) 0.0625

Explanation:
1. 25% of 25% = 0.25 × 0.25 = 0.0625.

Teacher's Note:
1. Convert each percentage to a decimal.
2. Then multiply.

Question 15: ?% of 932 + 30 = 309.6
(a) 25
(b) 30
(c) 35
(d) 40
Show Answer & Explanation

Answer: (b) 30

Explanation:
1. ?% of 932 = 309.6 − 30 = 279.6
2. ? = 279.6/932 × 100 = 30.

Teacher's Note:
1. Isolate the term with the unknown percentage.
2. Then divide by 932.

Question 16: √784 + ? = 78% of 500
(a) 342
(b) 352
(c) 362
(d) 372
Show Answer & Explanation

Answer: (c) 362

Explanation:
1. √784 = 28 and 78% of 500 = 390
2. ? = 390 − 28 = 362.

Teacher's Note:
1. Evaluate the root and the percentage separately.
2. Subtract to find the missing number.

Question 17: Two-fifths of one-third of three-sevenths of a number is 15. What is 40 percent of that number?
(a) 72
(b) 84
(c) 136
(d) None of these
Show Answer & Explanation

Answer: (d) None of these

Explanation:
1. (2/5)(1/3)(3/7) of N = 2N/35 = 15, so N = 262.5
2. 40% of N = 105, which is not among options (a) to (c).

Teacher's Note:
1. Multiply the fractions first.
2. Then take 40% of the number found.

Question 18: The difference between a number and its two-fifths is 510. What is 10% of that number?
(a) 12.75
(b) 85
(c) 204
(d) None of these
Show Answer & Explanation

Answer: (b) 85

Explanation:
1. N − 2N/5 = 3N/5 = 510, so N = 850
2. 10% of 850 = 85.

Teacher's Note:
1. Write the difference as a fraction of N.
2. Then find the percentage.

Question 19: A number, when 35 is subtracted from it, reduces to its 80 percent. What is four-fifths of that number?
(a) 70
(b) 90
(c) 120
(d) 140
Show Answer & Explanation

Answer: (d) 140

Explanation:
1. N − 35 = 0.8N, so 0.2N = 35 and N = 175
2. 4/5 of 175 = 140.

Teacher's Note:
1. The subtracted amount is 20% of the number.
2. Find N first.

Question 20: The sum of two numbers is 28/25 of the first number. The second number is what percent of the first?
(a) 12%
(b) 14%
(c) 16%
(d) 18%
Show Answer & Explanation

Answer: (a) 12%

Explanation:
1. Second = 28/25 − 1 = 3/25 of the first
2. 3/25 × 100 = 12%.

Teacher's Note:
1. Subtract the first number from the sum.
2. Convert the fraction to a percentage.

Question 21: If one number is 80% of the other and 4 times the sum of their squares is 656, then the numbers are
(a) 4, 5
(b) 8, 10
(c) 16, 20
(d) None of these
Show Answer & Explanation

Answer: (b) 8, 10

Explanation:
1. Let the numbers be 0.8b and b; sum of squares = 164
2. 0.64b² + b² = 164, so b² = 100 and b = 10
3. The numbers are 8 and 10.

Teacher's Note:
1. Express both numbers in terms of one variable.
2. Solve the quadratic in b².

Question 22: A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?
(a) 34%
(b) 44%
(c) 54%
(d) 64%
Show Answer & Explanation

Answer: (d) 64%

Explanation:
1. Correct result = 5/3 N and wrong result = 3/5 N
2. Error = (5/3 − 3/5)/(5/3) = (16/15) × (3/5) = 16/25 = 64%.

Teacher's Note:
1. Percentage error is measured against the correct value.
2. Use a common denominator for the fractions.

Question 23: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years age, which is 48. What is the total number of students in the school?
(a) 72
(b) 80
(c) 120
(d) None of these
Show Answer & Explanation

Answer: (d) None of these

Explanation:
1. Students above 8 years = 2/3 × 48 = 32
2. Students of 8 years or above = 48 + 32 = 80, which is 80% of the total
3. Total = 100, which is not among options (a) to (c).

Teacher's Note:
1. The below-8 group is 20%, so the rest is 80%.
2. Total = 80 × 100/80.

Question 24: If x is 80% of y, then what percent of 2x is y?
(a) 40%
(b) 62 1/2%
(c) 66 2/3%
(d) 80%
Show Answer & Explanation

Answer: (b) 62 1/2%

Explanation:
1. x = 0.8y, so 2x = 1.6y
2. y/2x = 1/1.6 = 0.625 = 62 1/2%.

Teacher's Note:
1. Express 2x in terms of y.
2. Then take the ratio y : 2x.

Question 25: A man spends 35% of his income on food, 25% on children's education and 80% of the remaining on house rent. What percent of his income is he left with?
(a) 8%
(b) 10%
(c) 12%
(d) 14%
Show Answer & Explanation

Answer: (a) 8%

Explanation:
1. Spent so far = 35% + 25% = 60%, remaining 40%
2. House rent = 80% of 40% = 32%
3. Left = 40% − 32% = 8%.

Teacher's Note:
1. Work with percentages of the income throughout.
2. The remaining 20% of 40% is saved.

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Percentage Objective Questions & Solutions for Class 10 Mathematics

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FAQs

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Are Assertion-Reasoning and Case-Study MCQs included in the Mathematics Class 10 material?

Yes, our CBSE Class 10 Mathematics Percentage MCQs Set 09 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the CBSE paper is now competency-based.

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