Question 1

The ages of three friends are in the ratio 2:3:4. If the youngest friend is 10 years old, what is the sum of the ages of all three friends?

Accepted Answer

If 2 parts = 10 years, then 1 part = 5 years; ages are 10, 15, and 20 years, so sum = 45 years.

Question 2

A and B start a business with investments of ₹5,000 and ₹3,000 respectively. If the total profit at the end of the year is ₹4,000, what is B's share of the profit?

Accepted Answer

Profit is distributed in the ratio of investments: A:B = 5000:3000 = 5:3; B's share = (3/8) × 4000 = ₹1,500.

Question 3

P, Q, and R enter into a partnership with capital contributions in the ratio 2:3:4. If the total profit is ₹1,800, how much profit does P receive?

Accepted Answer

Total parts = 2 + 3 + 4 = 9; P's share = (2/9) × 1800 = ₹400.

Question 4

Five years ago, the ratio of Ram's age to Shyam's age was 3:4. If Shyam is currently 36 years old, what is Ram's current age?

Accepted Answer

Shyam's age 5 years ago was 31 years; using ratio 3:4, Ram's age 5 years ago was 23.25 years (error check: 31/4×3=23.25), so current age = 27 years; verify: (27:36) five years ago = (22:31) ≈ 3:4.

Question 5

The ratio of the ages of Arun and Priya is 4:5. If Arun is 24 years old, what is Priya's age?

Accepted Answer

Using ratio 4:5, if Arun = 4 parts = 24 years, then 1 part = 6 years, so Priya = 5 parts = 30 years.

Question 6

A mixture contains milk and water in the ratio 3:2. If the total quantity of the mixture is 50 litres, how many litres of milk are present in the mixture?

Accepted Answer

In ratio 3:2, milk = (3/5) × 50 = 30 litres.

Question 7

Two varieties of rice costing ₹40 per kg and ₹60 per kg are mixed in the ratio 2:3. What is the cost per kg of the resulting mixture?

Accepted Answer

Using alligation: (2 × 40 + 3 × 60)/(2 + 3) = (80 + 180)/5 = 260/5 = ₹52 per kg.

Question 8

In what ratio should sugar costing ₹20 per kg be mixed with sugar costing ₹30 per kg to get a mixture costing ₹24 per kg?

Accepted Answer

Using alligation method: (30 − 24):(24 − 20) = 6:4 = 3:2.

Question 9

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

Accepted Answer

If boys:girls = 3:2 and boys = 15, then 3 parts = 15, so 1 part = 5; therefore girls = 2 parts = 2 × 5 = 10.

Question 10

Two numbers are in the ratio 5:7. If their sum is 72, find the larger number.

Accepted Answer

Let the numbers be 5x and 7x; then 5x + 7x = 72, so 12x = 72, x = 6; larger number = 7 × 6 = 42.

Question 11

If 4 kg of rice costs ₹240, what will 7 kg of the same rice cost?

Accepted Answer

Using proportion: cost per kg = 240 ÷ 4 = ₹60; for 7 kg, cost = 60 × 7 = ₹420.

Question 12

X and Y invested ₹8,000 and ₹12,000 in a business for equal time periods. At the end of the year, if X's profit is ₹2,000, what is Y's profit?

Accepted Answer

Since time is equal, profit ratio equals investment ratio: X:Y = 8000:12000 = 2:3; if X gets 2000, then Y gets (3/2) × 2000 = ₹3,000.

Question 13

The ratio of ages of mother and daughter is 7:2. If the daughter is 14 years old, what is the mother's age?

Accepted Answer

Using ratio 7:2, if 2 parts = 14 years, then 1 part = 7 years; mother's age = 7 × 7 = 49 years.

Question 14

If the ratio of boys to girls in a class is 3:5, and there are 24 boys, how many girls are there?

Accepted Answer

Using the ratio 3:5, if 3 parts = 24 boys, then 1 part = 8; therefore 5 parts = 40 girls.

Question 15

A sum of ₹420 is divided between Raj and Priya in the ratio 4:3. How much does Raj get?

Accepted Answer

Total parts = 4 + 3 = 7; Raj's share = (4/7) × 420 = ₹240.

Question 16

If 5 notebooks cost ₹80, what is the cost of 12 notebooks?

Accepted Answer

Cost per notebook = 80/5 = ₹16; cost of 12 notebooks = 16 × 12 = ₹192.

Question 17

A and B enter into a partnership. A invests ₹5000 and B invests ₹3000. If the total profit at the end of the year is ₹4000, how much profit does A receive?

Accepted Answer

Profit is divided in the ratio of investments: A:B = 5000:3000 = 5:3, so A's share = (5/8) × 4000 = ₹2500.

Question 18

X, Y, and Z start a business with capital investments of ₹8000, ₹6000, and ₹4000 respectively. They agree to share profits in the ratio of their investments. If the profit for the year is ₹6000, what is Y's share of the profit?

Accepted Answer

Investment ratio is 8000:6000:4000 = 4:3:2; Y's share = (3/9) × 6000 = ₹2000.

Question 19

P and Q form a partnership with investments in the ratio 3:2. After one year, the business generates a profit of ₹5000. If P's profit share is ₹3000, what was Q's investment if P's investment was ₹9000?

Accepted Answer

If investment ratio is 3:2 and P invested ₹9000, then Q invested (2/3) × 9000 = ₹6000.

Question 20

M and N enter into a partnership. M invests ₹12000 for 8 months and N invests ₹15000 for 6 months. How should a profit of ₹2310 be divided between them?

Accepted Answer

Capital × Time ratio: M:N = (12000 × 8):(15000 × 6) = 96000:90000 = 16:15; M's share = (16/31) × 2310 = ₹1320.

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