Question 1

X and Y form a partnership. X invests ₹12,000 for 8 months and Y invests ₹16,000 for 6 months. If the profit is ₹4,400, what is X's share?

Accepted Answer

Step 1: In partnerships with different time periods, profit is distributed in the ratio of (Capital × Time). X's contribution = 12,000 × 8 = 96,000. Y's contribution = 16,000 × 6 = 96,000. Step 2: Ratio X:Y = 96,000 : 96,000 = 1:1. Step 3: X's share = (1/2) × 4,400 = ₹2,200.

Question 2

A, B, and C invest ₹10,000, ₹15,000, and ₹20,000 respectively for equal time periods. The profit is ₹9,000. How much more profit does C get compared to A?

Accepted Answer

Step 1: Since time is equal, profit ratio = capital ratio = 10,000 : 15,000 : 20,000 = 2:3:4. Step 2: Total parts = 2 + 3 + 4 = 9. Step 3: A's share = (2/9) × 9,000 = ₹2,000. Step 4: C's share = (4/9) × 9,000 = ₹4,000. Step 5: Difference = 4,000 - 2,000 = ₹2,000.

Question 3

If 6 pens cost ₹90, what is the cost of 10 pens?

Accepted Answer

Step 1: Cost of 1 pen = 90 ÷ 6 = ₹15. Step 2: Cost of 10 pens = 15 × 10 = ₹150.

Question 4

P, Q, and R start a business with investments in the ratio 2:3:4. If the total profit is ₹18,000, what is R's profit share?

Accepted Answer

Step 1: Profit is distributed in the ratio of investments. P:Q:R = 2:3:4. Step 2: Total parts = 2 + 3 + 4 = 9. Step 3: R's share = (4/9) × 18,000 = ₹8,000.

Question 5

A sum of ₹1200 is divided between Raj and Priya in the ratio 3:5. How much does Priya get?

Accepted Answer

Step 1: Total parts = 3 + 5 = 8. Step 2: Priya's share = (5/8) × 1200 = 5 × 150 = ₹750.

Question 6

M and N invest ₹20,000 and ₹30,000 respectively in a business. After 1 year, M withdraws ₹5,000 and N adds ₹10,000. If the profit after 2 years is ₹12,000, what is M's profit share?

Accepted Answer

Step 1: M's capital-time product = (20,000 × 1) + (15,000 × 1) = 20,000 + 15,000 = 35,000. Step 2: N's capital-time product = (30,000 × 1) + (40,000 × 1) = 30,000 + 40,000 = 70,000. Step 3: Ratio M:N = 35,000 : 70,000 = 1:2. Step 4: Total parts = 3. Step 5: M's share = (1/3) × 12,000 = ₹4,000.

Question 7

Two containers have milk and water in ratios 3:1 and 5:3 respectively. If equal quantities from each container are mixed together, what is the ratio of milk to water in the final mixture?

Accepted Answer

Step 1: Container 1 has milk:water = 3:1, so in any quantity, milk fraction = 3/4, water fraction = 1/4. Step 2: Container 2 has milk:water = 5:3, so milk fraction = 5/8, water fraction = 3/8. Step 3: Let equal quantity = L litres from each. Step 4: Total milk = L(3/4) + L(5/8) = L(6/8 + 5/8) = L(11/8). Step 5: Total water = L(1/4) + L(3/8) = L(2/8 + 3/8) = L(5/8). Step 6: Ratio of milk to water = (11/8):(5/8) = 11:5.

Question 8

The ratio of ages of Aman and Bimal is 4:5. After 8 years, their ages will be in the ratio 6:7. What is Aman's current age?

Accepted Answer

Step 1: Let Aman's current age = 4x and Bimal's current age = 5x (from ratio 4:5). Step 2: After 8 years, Aman = 4x + 8 and Bimal = 5x + 8. Step 3: Future ratio is 6:7, so (4x+8):(5x+8) = 6:7. Step 4: Cross-multiply: 7(4x+8) = 6(5x+8) → 28x + 56 = 30x + 48. Step 5: Solve: 2x = 8 → x = 4. Step 6: Aman's current age = 4(4) = 16 years.

Question 9

The ratio of Chitra's age to Divya's age is 7:5. If the sum of their ages is 48 years, what is Divya's age?

Accepted Answer

Step 1: Let Chitra's age = 7x and Divya's age = 5x. Step 2: Given sum = 48, so 7x + 5x = 48. Step 3: 12x = 48 → x = 4. Step 4: Divya's age = 5(4) = 20 years.

Question 10

A shopkeeper mixes two types of rice costing ₹40 per kg and ₹60 per kg. In what ratio should they be mixed so that the cost of the mixture is ₹50 per kg?

Accepted Answer

Step 1: Use alligation method. Cost of cheaper rice = ₹40, cost of dearer rice = ₹60, cost of mixture = ₹50. Step 2: Difference between mixture cost and cheaper cost = 50 - 40 = 10. Step 3: Difference between dearer cost and mixture cost = 60 - 50 = 10. Step 4: Ratio of cheaper to dearer = 10:10 = 1:1.

Question 11

A container has 120 litres of a solution with alcohol and water in ratio 7:5. How much pure alcohol must be added to make the ratio 3:1?

Accepted Answer

Step 1: Original alcohol = 120 × (7/12) = 70 litres, water = 120 × (5/12) = 50 litres. Step 2: Let x litres of pure alcohol be added. Step 3: New alcohol = 70 + x, water remains 50 litres. Step 4: New ratio is 3:1, so (70 + x)/50 = 3/1. Step 5: 70 + x = 150 → x = 80 litres.

Question 12

Three containers have solutions with salt concentrations of 20%, 30%, and 50% respectively. If equal volumes are mixed from all three, what is the salt concentration in the final mixture?

Accepted Answer

Step 1: Let equal volume from each = V litres. Step 2: Salt from container 1 = V × 0.20 = 0.20V. Step 3: Salt from container 2 = V × 0.30 = 0.30V. Step 4: Salt from container 3 = V × 0.50 = 0.50V. Step 5: Total salt = 0.20V + 0.30V + 0.50V = 1.00V. Step 6: Total volume = V + V + V = 3V. Step 7: Concentration = (1.00V)/(3V) × 100% = (1.00/3) × 100% = 33.33% ≈ 33⅓%.

Question 13

Three years ago, Gita was twice as old as Hema. If Gita is currently 27 years old, what is Hema's current age?

Accepted Answer

Step 1: Gita's current age = 27 years. Step 2: Gita's age 3 years ago = 27 - 3 = 24 years. Step 3: Three years ago, Gita = 2 × Hema, so 24 = 2 × Hema (past). Step 4: Hema's age 3 years ago = 12 years. Step 5: Hema's current age = 12 + 3 = 15 years.

Question 14

A and B enter into a partnership with capital investments of ₹15,000 and ₹25,000 respectively. If the profit at the end of the year is ₹8,000, what is B's share of the profit?

Accepted Answer

Step 1: Profit is distributed in the ratio of capital investments. Ratio of A's capital to B's capital = 15,000 : 25,000 = 3 : 5. Step 2: Total parts = 3 + 5 = 8. Step 3: B's share = (5/8) × 8,000 = ₹5,000.

Question 15

Esha is 8 years older than Fiona. The ratio of their ages is 5:4. What is Esha's age?

Accepted Answer

Step 1: Let Esha's age = 5x and Fiona's age = 4x. Step 2: Given Esha is 8 years older: 5x - 4x = 8. Step 3: x = 8. Step 4: Esha's age = 5(8) = 40 years.

Question 16

If A:B = 7:5 and B:C = 5:3, then find A:B:C.

Accepted Answer

Step 1: A:B = 7:5 means A = 7k, B = 5k. Step 2: B:C = 5:3 means B = 5m, C = 3m. Step 3: Since B is common, 5k = 5m, so k = m. Step 4: Therefore A:B:C = 7k:5k:3k = 7:5:3.

Question 17

The ratio of ages of Aman and Bhuvan is 4:5. If Aman is 32 years old, what is Bhuvan's age?

Accepted Answer

Step 1: Let Aman's age = 4x and Bhuvan's age = 5x. Step 2: Given Aman = 32, so 4x = 32, therefore x = 8. Step 3: Bhuvan's age = 5x = 5 × 8 = 40 years.

Question 18

In a mixture, the ratio of milk to water is 7:2. If the mixture contains 28 litres of milk, how many litres of water are in the mixture?

Accepted Answer

Step 1: Let milk = 7x and water = 2x. Step 2: Given milk = 28, so 7x = 28, therefore x = 4. Step 3: Water = 2x = 2 × 4 = 8 litres.

Question 19

The ratio of boys to girls in a class is 5:3. If there are 40 boys, how many girls are there in the class?

Accepted Answer

Step 1: Let the common factor be x. Boys = 5x, Girls = 3x. Step 2: Given boys = 40, so 5x = 40, therefore x = 8. Step 3: Girls = 3x = 3 × 8 = 24.

Question 20

Two partners invest capital in the ratio 5:7. If the total capital is ₹48,000, and the profit is ₹9,600, what is the smaller partner's profit share?

Accepted Answer

Step 1: Capital ratio = 5:7. Total parts = 5 + 7 = 12. Step 2: Smaller partner's capital = (5/12) × 48,000 = ₹20,000. Step 3: Since time is equal, profit ratio = capital ratio = 5:7. Step 4: Smaller partner's profit = (5/12) × 9,600 = ₹4,000.

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