Question 1

What is 2.5 × 0.4?

Accepted Answer

Step 1: Multiply 2.5 × 0.4. Step 2: Ignore decimals temporarily: 25 × 4 = 100. Step 3: Count total decimal places: 2.5 has 1 decimal place, 0.4 has 1 decimal place, total = 2 decimal places. Step 4: Place decimal 2 places from the right in 100: 1.00 = 1. Therefore, the answer is 1.

Question 2

If 0.75 of a number is 120, what is the number?

Accepted Answer

Step 1: Let the number be x. Step 2: Set up equation: 0.75 × x = 120. Step 3: Convert 0.75 to fraction: 3/4 × x = 120. Step 4: Solve for x: x = 120 ÷ (3/4) = 120 × (4/3) = 480/3 = 160. Therefore, the number is 160.

Question 3

Express 7/20 as a decimal.

Accepted Answer

Step 1: To convert 7/20 to decimal, divide 7 by 20. Step 2: 7 ÷ 20 = 0.35. Alternatively, multiply numerator and denominator to make denominator 100: (7×5)/(20×5) = 35/100 = 0.35. Therefore, the answer is 0.35.

Question 4

If 5/6 of a tank holds 500 litres, what is the total capacity of the tank?

Accepted Answer

Step 1: Let the total capacity be x litres. Step 2: Set up equation: (5/6) × x = 500. Step 3: Solve for x: x = 500 ÷ (5/6) = 500 × (6/5) = 3000/5 = 600. Therefore, the total capacity is 600 litres.

Question 5

What is 3/5 of 2/3 of 150?

Accepted Answer

Step 1: Find 2/3 of 150 = (2/3) × 150 = 300/3 = 100. Step 2: Find 3/5 of 100 = (3/5) × 100 = 300/5 = 60. Alternatively: (3/5) × (2/3) × 150 = (6/15) × 150 = (2/5) × 150 = 60.

Question 6

A decimal number when multiplied by 8 gives 6.4. What is the decimal number?

Accepted Answer

Step 1: Let the decimal number be x. Then 8x = 6.4. Step 2: x = 6.4 ÷ 8 = 0.8.

Question 7

If 2.5 × a = 10, and 0.4 × b = 2, what is the value of a/b?

Accepted Answer

Step 1: From 2.5 × a = 10, we get a = 10 ÷ 2.5 = 4. Step 2: From 0.4 × b = 2, we get b = 2 ÷ 0.4 = 5. Step 3: a/b = 4/5 = 0.8.

Question 8

If 3/7 of a number is 48, what is 5/8 of that number?

Accepted Answer

Step 1: Let the number be x. Then (3/7)x = 48. Step 2: Solve for x: x = 48 × (7/3) = 112. Step 3: Find (5/8) of 112: (5/8) × 112 = 70. Therefore, the answer is 70.

Question 9

A shopkeeper mixes two types of flour. Type A costs ₹40 per kg and Type B costs ₹60 per kg. If he mixes them in the ratio 3:2, what is the cost per kg of the mixture?

Accepted Answer

Step 1: In ratio 3:2, for every 5 kg of mixture, 3 kg is Type A and 2 kg is Type B. Step 2: Cost of 3 kg Type A = 3 × 40 = ₹120. Step 3: Cost of 2 kg Type B = 2 × 60 = ₹120. Step 4: Total cost = 120 + 120 = ₹240 for 5 kg. Step 5: Cost per kg = 240 ÷ 5 = ₹48. Therefore, the answer is ₹48.

Question 10

A fraction when reduced to its simplest form is 7/9. If the numerator of the original fraction is 63, what is the denominator of the original fraction?

Accepted Answer

Step 1: The reduced fraction is 7/9. The original numerator is 63. Step 2: Find the multiplier: 63 ÷ 7 = 9. Step 3: The denominator of the original fraction = 9 × 9 = 81.

Question 11

A decimal number 0.abcabc... (where abc repeats) equals 7/27. If a, b, c are single digits with a ≠ 0, what is the value of a + b + c?

Accepted Answer

Step 1: Let x = 0.abcabcabc... = 0.̄abc̄ (repeating). Step 2: Multiply by 1000: 1000x = abc.abcabcabc... Step 3: Subtract: 1000x - x = abc → 999x = abc → x = abc/999. Step 4: Given x = 7/27, so abc/999 = 7/27. Step 5: Simplify 999 = 27 × 37, so abc/999 = abc/(27×37) = 7/27 → abc = 7 × 37 = 259. Step 6: Therefore a = 2, b = 5, c = 9 → a + b + c = 16.

Question 12

A decimal number 0.8̄3̄ (where both 8 and 3 repeat) is converted to a fraction. What is the numerator of this fraction in its simplest form?

Accepted Answer

Step 1: Let x = 0.838383... = 0.8̄3̄. Step 2: Multiply by 100: 100x = 83.838383... Step 3: Subtract: 100x - x = 83.838383... - 0.838383... → 99x = 83. Step 4: x = 83/99. Step 5: Check if 83/99 is in simplest form: GCD(83, 99) = 1 (83 is prime, 99 = 9 × 11). Step 6: Numerator is 83.

Question 13

If 2/5 of a number exceeds 1/3 of the same number by 18, what is 3/4 of that number?

Accepted Answer

Step 1: Let the number be n. Given: (2/5)n - (1/3)n = 18. Step 2: Find common denominator: (6/15)n - (5/15)n = 18. Step 3: (1/15)n = 18. Step 4: n = 270. Step 5: (3/4) × 270 = 810/4 = 202.5.

SSC CHSL Fractions & Decimals

Fractions & Decimals— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Fractions & Decimals — Practice Questions

60-Second Revision — Fractions & Decimals