Question 1

Express 0.625 as a fraction in its simplest form.

Accepted Answer

Step 1: Write 0.625 as 625/1000. Step 2: Find GCD(625, 1000) = 125. Step 3: Divide both by 125: 625÷125 = 5 and 1000÷125 = 8. Therefore, 0.625 = 5/8.

Question 2

If 2/5 of a number is 48, what is the number?

Accepted Answer

Step 1: Let the number be x. Step 2: Set up equation: (2/5)x = 48. Step 3: Multiply both sides by 5/2: x = 48 × (5/2) = 240/2 = 120. Therefore, the number is 120.

Question 3

If 3/7 of a tank is filled with water and the tank holds 280 litres, how many litres of water are in the tank?

Accepted Answer

Step 1: Water in tank = (3/7) × 280. Step 2: Calculate: (3 × 280)/7 = 840/7 = 120 litres. Therefore, there are 120 litres of water in the tank.

Question 4

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. Step 2: 8x = 6.4. Step 3: x = 6.4 ÷ 8 = 0.8.

Question 5

If 7/9 of a tank is filled with water and contains 630 litres, how many litres does the full tank hold?

Accepted Answer

Step 1: Let the full tank capacity be x litres. Step 2: (7/9)x = 630. Step 3: x = 630 × (9/7) = 90 × 9 = 810.

Question 6

If 2.5 kg of sugar costs ₹150, what is the cost of 4 kg of sugar?

Accepted Answer

Step 1: Cost per kg = 150 ÷ 2.5 = 60. Step 2: Cost of 4 kg = 60 × 4 = 240.

Question 7

The decimal representation of 7/12 is 0.58̄3̄ (where 3 repeats). If this decimal is multiplied by 144, what is the result?

Accepted Answer

Step 1: Convert 7/12 to decimal: 7 ÷ 12 = 0.583333... = 0.58̄3̄. Step 2: Multiply by 144: (7/12) × 144 = 7 × (144/12) = 7 × 12 = 84. Step 3: Alternatively, 0.58̄3̄ × 144 = (7/12) × 144 = 84. Therefore, the result is 84.

Question 8

If 2/3 of a number is 18 more than 1/4 of the same number, what is 5/6 of that number?

Accepted Answer

Step 1: Let the number be x. Step 2: Set up the equation: (2/3)x = (1/4)x + 18. Step 3: Rearrange: (2/3)x - (1/4)x = 18. Step 4: Find common denominator (12): (8/12)x - (3/12)x = 18 → (5/12)x = 18. Step 5: Solve for x: x = 18 × (12/5) = 216/5. Step 6: Find 5/6 of x: (5/6) × (216/5) = (5 × 216)/(6 × 5) = 216/6 = 36. Therefore, 5/6 of the number is 36.

Question 9

A fraction becomes 4/5 when 3 is subtracted from both numerator and denominator. The same fraction becomes 5/6 when 2 is added to both numerator and denominator. Find the original fraction.

Accepted Answer

Step 1: Let the fraction be x/y. Step 2: From first condition: (x-3)/(y-3) = 4/5, so 5(x-3) = 4(y-3) → 5x - 15 = 4y - 12 → 5x - 4y = 3. Step 3: From second condition: (x+2)/(y+2) = 5/6, so 6(x+2) = 5(y+2) → 6x + 12 = 5y + 10 → 6x - 5y = -2. Step 4: Solve simultaneously: From equation 1: 5x - 4y = 3. From equation 2: 6x - 5y = -2. Multiply first by 5 and second by 4: 25x - 20y = 15 and 24x - 20y = -8. Subtract: x = 23. Step 5: Substitute x = 23 in 5x - 4y = 3: 115 - 4y = 3 → y = 28. Therefore, the fraction is 23/28.

Question 10

A decimal number 0.3̄6̄ (where both 3 and 6 repeat) is converted to a fraction. What is the denominator of this fraction when expressed in lowest terms?

Accepted Answer

Step 1: Let x = 0.3̄6̄ = 0.363636... Step 2: Multiply by 100: 100x = 36.363636... Step 3: Subtract: 100x - x = 36.363636... - 0.363636... → 99x = 36. Step 4: Solve for x: x = 36/99. Step 5: Reduce to lowest terms: GCD(36, 99) = 9. So x = (36÷9)/(99÷9) = 4/11. Step 6: The denominator in lowest terms is 11.

SSC CPO Fractions & Decimals

SSC CPO Fractions & Decimals — Past Exam Questions

Fractions & Decimals— Rules & Concept

Key Points to Remember

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60-Second Revision — Fractions & Decimals