Question 1

A mixture of 60 litres contains milk and water in the ratio 2:1. How much water should be added to make the ratio 1:1?

Accepted Answer

Step 1: Current ratio = 2:1, total parts = 3. Milk = (2/3) × 60 = 40 litres. Water = (1/3) × 60 = 20 litres. Step 2: Let x litres of water be added. New water = 20 + x. Step 3: For ratio 1:1, Milk = Water. Step 4: 40 = 20 + x → x = 20 litres.

Question 2

In a partnership, A and B's capital contributions are in the ratio 5:3. If A's profit share is ₹8,000, what is the total profit?

Accepted Answer

Step 1: Ratio A:B = 5:3. Step 2: Total parts = 5 + 3 = 8. Step 3: A's share is 5 parts out of 8. Step 4: If (5/8) × Total Profit = 8,000, then Total Profit = 8,000 × (8/5) = ₹12,800.

Question 3

Two containers have alcohol solutions of 30% and 50% respectively. In what ratio should they be mixed to get a 40% alcohol solution?

Accepted Answer

Step 1: Use alligation method. Desired concentration = 40%. Step 2: Difference between 50% and 40% = 10. Difference between 40% and 30% = 10. Step 3: Ratio = (Difference from higher):(Difference from lower) = 10:10 = 1:1. Step 4: Mix equal quantities of both solutions to get 40% concentration.

Question 4

A shopkeeper mixes two types of rice costing ₹40 per kg and ₹60 per kg in the ratio 3:2. At what price per kg should he sell the mixture to make a 25% profit?

Accepted Answer

Step 1: Cost price of mixture per kg using weighted average. Ratio = 3:2, total parts = 5. Step 2: Cost = (3 × 40 + 2 × 60)/5 = (120 + 120)/5 = 240/5 = ₹48 per kg. Step 3: For 25% profit, Selling Price = Cost Price × (1 + 25/100) = 48 × 1.25 = ₹60 per kg.

Question 5

A chemist has two solutions of acid with concentrations 25% and 75%. In what ratio should they be mixed to obtain a 60% acid solution?

Accepted Answer

Step 1: Use alligation method. Desired concentration = 60%. Step 2: Difference between 75% and 60% = 15. Difference between 60% and 25% = 35. Step 3: Ratio = (Difference from higher):(Difference from lower) = 15:35 = 3:7. Step 4: Mix the 75% solution and 25% solution in ratio 3:7.

Question 6

X, Y, and Z form a partnership with capital contributions in the ratio 3:4:5. If the total profit at the end of the year is ₹36,000, what is Z's profit share?

Accepted Answer

Step 1: Ratio of contributions = 3:4:5. Step 2: Total parts = 3 + 4 + 5 = 12. Step 3: Z's share = (5/12) × 36,000 = ₹15,000.

Question 7

If A:B = 2:3 and B:C = 4:5, what is A:C?

Accepted Answer

Step 1: A:B = 2:3 and B:C = 4:5. Step 2: To combine, make B the same in both ratios. LCM(3,4) = 12. Step 3: A:B = 2:3 = 8:12 and B:C = 4:5 = 12:15. Step 4: Therefore, A:B:C = 8:12:15, so A:C = 8:15.

Question 8

A sum of money is divided between X and Y in the ratio 4:6. If X receives ₹800, what is the total sum?

Accepted Answer

Step 1: X:Y = 4:6. Let X = 4k and Y = 6k. Step 2: Given X = 800, so 4k = 800 ⟹ k = 200. Step 3: Total sum = 4k + 6k = 10k = 10 × 200 = ₹2000.

Question 9

The ages of Ravi and Sita are in the ratio 7:5. After 6 years, their ages will be in the ratio 4:3. What is Ravi's current age?

Accepted Answer

Step 1: Let Ravi's current age = 7x and Sita's current age = 5x. Step 2: After 6 years, Ravi's age = 7x + 6 and Sita's age = 5x + 6. Step 3: Given that after 6 years, their ratio = 4:3, so (7x + 6)/(5x + 6) = 4/3. Step 4: Cross-multiply: 3(7x + 6) = 4(5x + 6). Step 5: 21x + 18 = 20x + 24. Step 6: x = 6. Step 7: Ravi's current age = 7x = 7(6) = 42 years.

Question 10

The ratio of boys to girls in a class is 3:2. If there are 15 boys, how many girls are there?

Accepted Answer

Step 1: Boys:Girls = 3:2. Let boys = 3m and girls = 2m. Step 2: Given boys = 15, so 3m = 15 ⟹ m = 5. Step 3: Girls = 2m = 2 × 5 = 10.

Question 11

The ratio of Aman's age to Bimal's age is 3:2. If the sum of their ages is 60 years, what will be the ratio of their ages after 10 years?

Accepted Answer

Step 1: Let Aman's age = 3x and Bimal's age = 2x. Step 2: Sum of their ages = 3x + 2x = 60. Step 3: 5x = 60, so x = 12. Step 4: Aman's current age = 3(12) = 36 years and Bimal's current age = 2(12) = 24 years. Step 5: After 10 years, Aman's age = 36 + 10 = 46 years and Bimal's age = 24 + 10 = 34 years. Step 6: Ratio after 10 years = 46:34 = 23:17.

Question 12

The ratio of the present ages of Arun and Bhavna is 5:3. If Arun is 20 years older than Bhavna, what is Bhavna's present age?

Accepted Answer

Step 1: Let Arun's age = 5x and Bhavna's age = 3x (from ratio 5:3). Step 2: Given that Arun is 20 years older than Bhavna, so 5x - 3x = 20. Step 3: 2x = 20, therefore x = 10. Step 4: Bhavna's age = 3x = 3(10) = 30 years.

Question 13

Chitra's age is 4 times Deepti's age. If Chitra is 36 years old, what was the ratio of their ages 6 years ago?

Accepted Answer

Step 1: Chitra's current age = 36 years. Step 2: Chitra's age = 4 × Deepti's age, so 36 = 4 × Deepti's age. Step 3: Deepti's current age = 36/4 = 9 years. Step 4: Six years ago, Chitra's age = 36 - 6 = 30 years. Step 5: Six years ago, Deepti's age = 9 - 6 = 3 years. Step 6: Ratio of their ages 6 years ago = 30:3 = 10:1.

Question 14

A and B enter into a partnership. A invests ₹24,000 and B invests ₹36,000. After one year, the profit is ₹15,000. What is B's share of the profit?

Accepted Answer

Step 1: Find the ratio of investments: A : B = 24,000 : 36,000 = 2 : 3. Step 2: Total parts = 2 + 3 = 5. Step 3: B's share = (3/5) × 15,000 = ₹9,000.

Question 15

The ratio of Esha's age to Fiona's age is 5:4. If Esha is 15 years older than Fiona, what will be their combined age after 5 years?

Accepted Answer

Step 1: Let Esha's age = 5x and Fiona's age = 4x. Step 2: Esha is 15 years older than Fiona, so 5x - 4x = 15. Step 3: x = 15. Step 4: Esha's current age = 5(15) = 75 years and Fiona's current age = 4(15) = 60 years. Step 5: After 5 years, Esha's age = 75 + 5 = 80 years and Fiona's age = 60 + 5 = 65 years. Step 6: Combined age after 5 years = 80 + 65 = 145 years.

Question 16

Two numbers are in the ratio 5:8. If their difference is 24, what is the larger number?

Accepted Answer

Step 1: Let the numbers be 5x and 8x. Step 2: Difference = 8x - 5x = 3x = 24. Step 3: x = 8. Step 4: Larger number = 8x = 8 × 8 = 64.

Question 17

Five years ago, the ratio of Priya's age to Deepak's age was 4:5. If Deepak is currently 35 years old, what is Priya's current age?

Accepted Answer

Step 1: Deepak's current age = 35 years. Step 2: Five years ago, Deepak's age = 35 - 5 = 30 years. Step 3: Five years ago, ratio of Priya's age to Deepak's age = 4:5. Step 4: If Deepak's age five years ago was 30, and the ratio is 4:5, then Priya's age five years ago = (4/5) × 30 = 24 years. Step 5: Priya's current age = 24 + 5 = 29 years.

Question 18

The ratio of ages of A and B is 5:7. If A's age is 25 years, what is B's age?

Accepted Answer

Step 1: Let A's age = 5x and B's age = 7x. Step 2: Given A's age = 25, so 5x = 25, which gives x = 5. Step 3: B's age = 7x = 7 × 5 = 35 years.

Question 19

If 3 pens cost ₹45, how much will 8 pens cost?

Accepted Answer

Step 1: Cost of 1 pen = 45 ÷ 3 = ₹15. Step 2: Cost of 8 pens = 15 × 8 = ₹120.

Question 20

M, N, and O invest ₹20,000, ₹30,000, and ₹50,000 respectively in a business. After 1 year, the profit is ₹40,000. What is the difference between O's and M's profit shares?

Accepted Answer

Step 1: Ratio of investments M:N:O = 20,000:30,000:50,000 = 2:3:5. Step 2: Total parts = 2 + 3 + 5 = 10. Step 3: M's share = (2/10) × 40,000 = ₹8,000. Step 4: O's share = (5/10) × 40,000 = ₹20,000. Step 5: Difference = 20,000 - 8,000 = ₹12,000.

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