Question 1

What is 7/9 ÷ 14/27?

Accepted Answer

Step 1: Division of fractions: (7/9) ÷ (14/27) = (7/9) × (27/14). Step 2: Multiply: (7 × 27)/(9 × 14) = 189/126. Step 3: Simplify by GCD(189,126) = 63: 189÷63 = 3, 126÷63 = 2. Therefore, 3/2.

Question 2

Express 0.625 as a fraction in its simplest form.

Accepted Answer

Step 1: Write 0.625 = 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 3

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

Accepted Answer

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

Question 4

What is the decimal equivalent of 7/20?

Accepted Answer

Step 1: Convert 7/20 to a decimal by dividing 7 by 20. Step 2: 7 ÷ 20 = 0.35. Alternatively, multiply numerator and denominator by 5: (7×5)/(20×5) = 35/100 = 0.35.

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: Simplify: (75÷25)/(100÷25) = 3/4. The denominator is 4.

Question 6

If 2/5 of a number is 24, what is the number?

Accepted Answer

Step 1: Let the number be x. Then (2/5) × x = 24. Step 2: Multiply both sides by 5/2: x = 24 × (5/2) = 120/2 = 60.

Question 7

What is 7/9 ÷ 14/27?

Accepted Answer

Step 1: Division of fractions: (7/9) ÷ (14/27) = (7/9) × (27/14). Step 2: Multiply: (7 × 27)/(9 × 14) = 189/126. Step 3: Simplify by GCD(189, 126) = 63: 189÷63 = 3, 126÷63 = 2. Answer: 3/2.

Question 8

If 2/5 of a number is 24, what is the number?

Accepted Answer

Step 1: Let the number be x. Then (2/5)x = 24. Step 2: Multiply both sides by 5/2: x = 24 × (5/2) = 120/2 = 60.

Question 9

Express 0.625 as a fraction in its simplest form.

Accepted Answer

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

Question 10

Subtract 0.375 from 1.5. What is the result?

Accepted Answer

Step 1: Align decimals: 1.500 - 0.375. Step 2: Subtract from right to left: 0 - 5 requires borrowing. After borrowing: 10 - 5 = 5 (thousandths), 9 - 7 = 2 (hundredths), 4 - 3 = 1 (tenths), 1 - 0 = 1 (ones). Step 3: Result is 1.125.

Question 11

Express 0.625 as a fraction in simplest form.

Accepted Answer

Step 1: Write 0.625 as a fraction with denominator as a power of 10: 0.625 = 625/1000. Step 2: Find GCD(625, 1000). 625 = 5⁴ and 1000 = 2³ × 5³, so GCD = 5³ = 125. Step 3: Divide both numerator and denominator by 125: (625 ÷ 125)/(1000 ÷ 125) = 5/8. Therefore, the answer is 5/8.

Question 12

If 5/6 of a number is 50, what is the number?

Accepted Answer

Step 1: Let the number be x. Then (5/6)x = 50. Step 2: Multiply both sides by 6/5: x = 50 × (6/5) = 300/5 = 60.

Question 13

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 14

If 2.5 metres of cloth costs ₹187.50, what is the cost of 6 metres of the same cloth?

Accepted Answer

Step 1: Find the cost per metre: Cost per metre = 187.50 / 2.5 = 75 per metre. Step 2: Find cost of 6 metres: 6 × 75 = 450. Therefore, the cost of 6 metres is ₹450.

Question 15

If 2.5 × a = 15, and 3/4 × b = 15, what is the ratio of a to b?

Accepted Answer

Step 1: Solve for a: 2.5 × a = 15, so a = 15/2.5 = 6. Step 2: Solve for b: (3/4) × b = 15, so b = 15 × (4/3) = 20. Step 3: Ratio a:b = 6:20 = 3:10.

Question 16

What is the difference between 0.75 and 3/5 expressed as a decimal?

Accepted Answer

Step 1: Convert 3/5 to decimal: 3/5 = 0.6. Step 2: Find the difference: 0.75 − 0.6 = 0.15. Therefore, the answer is 0.15.

Question 17

A number when divided by 0.5 gives 84. What is the number when expressed as a decimal?

Accepted Answer

Step 1: Let the number be x. According to the problem: x ÷ 0.5 = 84. Step 2: Dividing by 0.5 is equivalent to multiplying by 2 (since 1/0.5 = 2). So x × 2 = 84. Step 3: Therefore, x = 84/2 = 42. The number is 42.0.

Question 18

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 by weight, what is the cost per kg of the mixture as a decimal?

Accepted Answer

Step 1: Let the quantities be 3x kg of Type A and 2x kg of Type B. Step 2: Cost of Type A = 3x × 40 = 120x. Cost of Type B = 2x × 60 = 120x. Step 3: Total cost = 120x + 120x = 240x. Total weight = 3x + 2x = 5x. Step 4: Cost per kg = 240x / 5x = 240/5 = 48. Therefore, the cost per kg of the mixture is ₹48.0.

Question 19

A fraction becomes 4/5 when 1 is subtracted from both numerator and denominator. When 5 is added to both numerator and denominator, the fraction becomes 5/6. Find the original fraction.

Accepted Answer

Step 1: Let the original fraction be x/y. From the first condition: (x-1)/(y-1) = 4/5, so 5(x-1) = 4(y-1), giving 5x - 5 = 4y - 4, or 5x - 4y = 1. Step 2: From the second condition: (x+5)/(y+5) = 5/6, so 6(x+5) = 5(y+5), giving 6x + 30 = 5y + 25, or 6x - 5y = -5. Step 3: Solve the system: 5x - 4y = 1 and 6x - 5y = -5. Multiply first equation by 5 and second by 4: 25x - 20y = 5 and 24x - 20y = -20. Subtract: x = 25. Step 4: Substitute x = 25 into 5x - 4y = 1: 125 - 4y = 1, so 4y = 124, y = 31. The original fraction is 25/31.

Question 20

The sum of a decimal number and its reciprocal is 2.9. If the decimal number is greater than 1, what is the decimal number?

Accepted Answer

Step 1: Let the decimal number be x. According to the problem: x + 1/x = 2.9. Step 2: Multiply both sides by x: x² + 1 = 2.9x, or x² - 2.9x + 1 = 0. Step 3: Convert to 10x² - 29x + 10 = 0. Step 4: Discriminant = 841 - 400 = 441 = 21². Step 5: x = (29 ± 21)/20, so x = 2.5 or x = 0.4. Since x > 1, answer is 2.5.

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