Question 1

What is 2/5 of 150?

Accepted Answer

Step 1: To find 2/5 of 150, multiply: (2/5) × 150. Step 2: Calculate: (2 × 150)/5 = 300/5 = 60. Therefore, the answer is 60.

Question 2

Subtract 0.45 from 1.2. What is the result?

Accepted Answer

Step 1: Align the decimal points: 1.20 - 0.45. Step 2: Subtract from right to left: 0 - 5 requires borrowing, so it becomes 10 - 5 = 5. Step 3: 1 - 4 (after borrowing) = -3, so borrow from the units place: 11 - 4 = 7, and 1 - 1 = 0. Step 4: Result is 0.75.

Question 3

Express 0.45 as a fraction in lowest terms.

Accepted Answer

Step 1: Write 0.45 as 45/100. Step 2: Find GCD(45, 100) = 5. Step 3: Divide both by 5: 45÷5 = 9, 100÷5 = 20. Therefore, 0.45 = 9/20.

Question 4

Subtract 2/5 from 4/5. What is the result?

Accepted Answer

Step 1: Both fractions have the same denominator (5). Step 2: Subtract numerators: 4/5 - 2/5 = (4-2)/5 = 2/5. Therefore, the answer is 2/5.

Question 5

If 0.75 is expressed as a fraction in lowest terms, what is the denominator?

Accepted Answer

Step 1: Write 0.75 as 75/100. Step 2: Find GCD of 75 and 100, which is 25. Step 3: Divide both by 25: (75÷25)/(100÷25) = 3/4. Step 4: The denominator is 4.

Question 6

Express 7/20 as a decimal.

Accepted Answer

Step 1: Convert the fraction 7/20 to decimal by dividing 7 by 20. Step 2: 7 ÷ 20 = 0.35. Alternatively, multiply numerator and denominator by 5 to get 35/100 = 0.35. Therefore, the answer is 0.35.

Question 7

If 7/9 of a number is 63, what is the number?

Accepted Answer

Step 1: Let the number be x. Then (7/9) × x = 63. Step 2: Multiply both sides by 9/7: x = 63 × (9/7). Step 3: x = (63 × 9)/7 = 567/7 = 81. Therefore, the number is 81.

Question 8

Convert 0.625 to 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, 1000÷125 = 8. Therefore, 0.625 = 5/8.

Question 9

A shopkeeper mixes two types of rice: Type A at ₹40 per kg and Type B at ₹60 per kg. If the mixture is sold at ₹55 per kg and the profit is 10%, what is the ratio of Type A to Type B in the mixture?

Accepted Answer

Step 1: Let the cost price of the mixture be C. Since profit = 10%, selling price = 1.1C. Given selling price = ₹55, so 1.1C = 55, thus C = 50 per kg. Step 2: Use the alligation method. Cost price of mixture = ₹50. Type A costs ₹40, Type B costs ₹60. Step 3: Difference from A to mixture = 50 - 40 = 10. Difference from mixture to B = 60 - 50 = 10. Step 4: Ratio of A to B = 10 : 10 = 1 : 1.

Question 10

A shopkeeper mixes two types of rice. 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 (rounded to nearest rupee)?

Accepted Answer

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

Question 11

If 7/8 of a number is equal to 5/6 of another number, and the difference between the two numbers is 12, what is the larger number?

Accepted Answer

Step 1: Let the two numbers be x and y. Given: (7/8)x = (5/6)y. Step 2: From this, 7x/8 = 5y/6, so 42x = 40y (cross-multiply), thus 21x = 20y, or y = (21/20)x. Step 3: Given the difference is 12. Since y = (21/20)x and 21/20 > 1, we have y > x, so y - x = 12. Step 4: (21/20)x - x = 12, so (21/20 - 20/20)x = 12, thus (1/20)x = 12, so x = 240. Step 5: y = 240 + 12 = 252. Verify: (7/8) × 240 = 210 and (5/6) × 252 = 210 ✓.

Question 12

A number when divided by 3/5 gives 50. What is the number when divided by 5/3?

Accepted Answer

Step 1: Let the number be x. Given x ÷ (3/5) = 50, so x × (5/3) = 50, thus x = 50 × (3/5) = 30. Step 2: Now divide this number by 5/3: 30 ÷ (5/3) = 30 × (3/5) = 18. Therefore, the answer is 18.

Question 13

A shopkeeper mixes 2.5 kg of sugar costing ₹40 per kg with 1.5 kg of sugar costing ₹60 per kg. What is the cost price per kg of the mixture?

Accepted Answer

Step 1: Cost of first sugar = 2.5 × 40 = ₹100. Step 2: Cost of second sugar = 1.5 × 60 = ₹90. Step 3: Total cost = 100 + 90 = ₹190. Step 4: Total quantity = 2.5 + 1.5 = 4 kg. Step 5: Cost per kg = 190/4 = ₹47.50.

Question 14

If 0.75 of a tank is filled with water and 0.2 of the remaining capacity is filled with oil, what fraction of the tank is now empty?

Accepted Answer

Step 1: Water fills 0.75 of the tank, so remaining capacity = 1 - 0.75 = 0.25. Step 2: Oil fills 0.2 of the remaining capacity = 0.2 × 0.25 = 0.05 of the tank. Step 3: Total filled = 0.75 + 0.05 = 0.80. Step 4: Empty fraction = 1 - 0.80 = 0.20 = 1/5.

Question 15

The product of two fractions is 3/8. One fraction is 2/3 of the other. Find the larger fraction.

Accepted Answer

Step 1: Let the larger fraction be x. Then the smaller fraction is (2/3)x. Step 2: Their product: x × (2/3)x = 3/8, which gives (2/3)x² = 3/8. Step 3: Solve for x²: x² = (3/8) × (3/2) = 9/16. Step 4: Therefore, x = 3/4 (taking positive root). Step 5: Verify: (3/4) × (2/3 × 3/4) = (3/4) × (1/2) = 3/8 ✓. The larger fraction is 3/4.

Question 16

A decimal number when multiplied by 0.8 gives 3.2. When this number is divided by 0.4, what is the result?

Accepted Answer

Step 1: Let the decimal number be x. Then x × 0.8 = 3.2. Step 2: Solve for x: x = 3.2 ÷ 0.8 = 4. Step 3: Now divide this number by 0.4: 4 ÷ 0.4 = 10. Therefore, the answer is 10.

Question 17

If 3/5 of a number is equal to 4/7 of another number, and the second number is 35, what is 2/3 of the first number?

Accepted Answer

Step 1: Let the first number be x and the second number be 35. Then (3/5)x = (4/7) × 35. Step 2: Simplify the right side: (4/7) × 35 = 4 × 5 = 20. Step 3: Solve for x: (3/5)x = 20 → x = 20 × (5/3) = 100/3. Step 4: Find (2/3) of x: (2/3) × (100/3) = 200/9. Therefore, the answer is 200/9 or 22 2/9.

Question 18

A number consists of two decimal places. When 0.36 is subtracted from it, the result is 1.5 times the original number divided by 2. Find the original number.

Accepted Answer

Step 1: Let the original number be x. Step 2: According to the problem: x − 0.36 = (1.5 × x)/2 = 0.75x. Step 3: Rearrange: x − 0.75x = 0.36. Step 4: Simplify: 0.25x = 0.36. Step 5: Solve: x = 0.36/0.25 = 1.44. Step 6: Verify: 1.44 − 0.36 = 1.08, and 0.75 × 1.44 = 1.08 ✓. Therefore, the original number is 1.44.

Question 19

A number when divided by 7/9 gives 63. When this number is divided by 9/7, what will be the result?

Accepted Answer

Step 1: Let the number be x. Given: x ÷ (7/9) = 63. Step 2: This means x × (9/7) = 63. Step 3: Solving for x: x = 63 × (7/9) = (63 × 7)/9 = 441/9 = 49. Step 4: Now find x ÷ (9/7) = 49 × (7/9) = (49 × 7)/9 = 343/9 = 38 1/9. Alternatively: If x ÷ (7/9) = 63, then x × (9/7) = 63, so x = 49. Then x ÷ (9/7) = 49 × (7/9) = 343/9 = 38 1/9.

RRB NTPC Fractions & Decimals

Fractions & Decimals— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Fractions & Decimals — Practice Questions

60-Second Revision — Fractions & Decimals