Free Basic Mathematics: Fractions, Percentages, Ratios and Indices MCQs with Answers

• A. 9/8
• B. 13/8
• C. 11/8
• D. 15/8

Explanation: Convert 3/4 to 6/8, then add 5/8 to obtain 11/8. The common denominator is 8, not 4 or 16.

• A. 200
• B. 220
• C. 240
• D. 260

Explanation: Since 20% equals 0.20, the number is 48 divided by 0.20, which gives 240. Multiplying 48 by 20 would incorrectly treat 20% as 20.

• A. Rs. 36
• B. Rs. 32
• C. Rs. 28
• D. Rs. 42

Explanation: The total ratio is 7 parts, so one part equals 84 divided by 7, or 12. The smaller share is 3 times 12, equal to Rs. 36.

• A. 8
• B. 12
• C. 16
• D. 32

Explanation: For the same base, exponents are added during multiplication and subtracted during division.

• A. 1/4
• B. 5/12
• C. 3/8
• D. 7/16

Explanation: The decimal 0.375 equals 375/1000, which simplifies to 3/8. The other fractions produce different decimal values.

• A. 15%
• B. 20%
• C. 25%
• D. 30%

Explanation: The increase is Rs. 50, and 50 divided by 250 equals 0.20. Therefore, the percentage increase is 20%, not 25% of the new price.

• A. 8:12:15
• B. 6:8:10
• C. 8:10:15
• D. 12:8:15

Explanation: Make the value of B common by using 12. The first ratio becomes 8:12 and the second becomes 12:15, giving A:B:C = 8:12:15.

• A. -8
• B. 8
• C. 1/8
• D. -1/8

Explanation: A negative exponent takes the reciprocal of the base, so (1/2)^(-3) equals 2^3. Therefore, the value is 8, not negative 8.

• A. Rs. 782
• B. Rs. 816
• C. Rs. 800
• D. Rs. 840

Explanation: After a 15% discount, the selling price represents 85% of the original price.

• A. 2
• B. 3
• C. 4
• D. 5

Explanation: Since 81 equals 3^4, the exponents must satisfy x + 1 = 4. Solving this equation gives x = 3.

• A. 1/9
• B. 2/9
• C. 1/3
• D. 5/9

Explanation: Convert 2/3 to 6/9, then subtract it from 7/9 to obtain 1/9. The common denominator is needed before subtracting fractions.

• A. 54
• B. 60
• C. 64
• D. 66

Explanation: Divide 72 by 6 to get 12, then multiply 12 by 5. Therefore, 5/6 of 72 equals 60.

• A. 4.5%
• B. 45%
• C. 0.45%
• D. 450%

Explanation: To convert a decimal to a percentage, multiply it by 100. Thus, 0.45 becomes 45%, not 0.45% or 450%.

• A. 18
• B. 20
• C. 24
• D. 28

Explanation: The total number of ratio parts is 12, so each part represents 48 ÷ 12 = 4 students. Boys represent 5 parts, giving 5 × 4 = 20.

• A. Rs. 120
• B. Rs. 160
• C. Rs. 140
• D. Rs. 180

Explanation: The ratio contains 9 total parts, and each part is Rs. 360 ÷ 9 = Rs. 40. The largest share has 4 parts, so it is Rs. 160.

• A. 24
• B. 30
• C. 36
• D. 40

Explanation: Since 12.5% equals 1/8, calculate 240 ÷ 8. The result is 30.

• A. 3
• B. 6
• C. 9
• D. 12

Explanation: When powers with the same base are divided, subtract the exponents: 3^(4−2) = 3^2. Therefore, the value is 9.

• A. x^6
• B. x^5
• C. x^8
• D. 2x^3

Explanation: When a power is raised to another power, multiply the exponents. Thus, (x^3)^2 equals x^(3×2), or x^6.

• A. 10%
• B. 12%
• C. 15%
• D. 20%

Explanation: The profit is Rs. 575 − Rs. 500 = Rs. 75. Dividing Rs. 75 by the cost price of Rs. 500 and multiplying by 100 gives a 15% profit.

• A. 3/10
• B. 1/2
• C. 3/5
• D. 7/10

Explanation: Convert 2/5 to 4/10, then add 1/10 to get 5/10. Simplifying 5/10 gives 1/2.