**Qu.1) The capital of A and B are Rs. 20,000 and Rs.4,000 respectively. A is entitled to be paid a salary of Rs.1,200 per annum being a working partner. If the gross profit for one year is Rs. 1,800, their shares in the profit are respectively :**

**Sol**. Given: Capital Ratio of A and B = 20,000: 4000 = 5: 1

Salary of A = Rs. 1200

Gross profit for 1 year = Rs. 1800

Remaining profit = Rs. 1800 – Rs. 1200 = Rs. 600

(5 + 1) units = 600

6 units = 600

1 unit = 600/ 6 = Rs. 100

Share of A = 5 x 100 = Rs. 500

Share of B = 100 x 1 = Rs. 100

Total share of A = 1200 + 500 = Rs. 1700

Total share of B = 1800 – 1700 = Rs. 100

**Ans. Their shares of profit is 1700 and 100 respectively**

**Qu.2) A and B are partners who share profit in the ratio of 3: 2, They agree to take C into partnership of 1/4 ^{th} share of profit. The new profit-sharing ratio will be:**

**Sol**. Let the total share be 100 units

Ratio of C = 100/ 4 = 25 units

Remaining shares = 100 – 25 units = 75 units

Share of A = [75/ (3 + 2)] x 3 = 45 units

Share of B = [75/ (3 + 2)] x 2 = 30 units

Therefore their profit ratio = A : B : C = 45: 30: 25

= 9: 6: 5

**Ans, the new profit sharing will be 9: 6: 5**

**Qu.3) A, B and C jointly start a business A puts in Rs.15,000 for 8 months, B puts in Rs. 12,000 for 9 months and C puts in Rs. 8,000, for the whole year. At the end of the year there is a profit of Rs. 10,800. The difference between A’s share and C’s share in the profit will be :**

**Sol**. Given: Capital ratio = A: B: C = 15000: 12000: 8000

Time Ratio = 8: 9: 12

As we know that, CT = P

P1 = C1.T1 = 15000 x 8 = 120000

P2 = C2. T2 = 12000 x 9 = 108000

P3 = C3. T3 = 8000 x 12 = 96000

Profit ratio = P1 : P2: P3 = 120: 108: 96 = 10: 9: 8

According to the question, (10 + 9 + 8) units = 10800

27 units = 10800

1 unit = Rs. 400

Difference between share of A and C = (10 – 8) x 400

= 2 x 400 = Rs. 800

**Ans. The difference between share of A and C is Rs. 800.**

**Qu.4) A started a business by investing Rs. 50,000. After 6 months B joined her by investing Rs. 75,000. After 6 months C joined with Rs. 1,25,000. What is the ratio of profit shared after 2 years among A, B and C?**

**Sol**. Given: Ratio of their Capital = A: B: C = 50000: 75000: 125000

Ratio of time = 24: 18: 12 = 2: 3/2 : 1

Profit Ratio-

P1 = C1.T1 = 50000 x 2 = 100000

P2 = C2. T2 = 75000 x 3/2 = 112500

P3 = C3. T3 = 125000 x 1 = 125000

P1: P2: P3 = 8: 9: 10

**Ans. Required ratio of profit = 8: 9: 10**

**Qu.5) Three partners A, B and C started a business by investing. 48000 each. After 6 months, A left the business, after 10 months B left the business and after 12 months C left the business. If total earned profit is . 5250, then find the share of A, B and C?**

**Sol.** Given: Ratio of their capital = 48000: 48000: 48000 = 1: 1:1

Ratio of time = 6: 10: 12 = 3: 5: 6

Here capital is same so the profit is divided in the ratio if their time

According to their time, (3 + 5 + 6) units = 14 units

14 units = 5250

1 unit = 5250/ 14 = 375

Therefore share of A = 375 x 3 = 1125

Share of B = 375 x 5 = 1875

Share of C = 375 x 6 = 2250

**Ans. Their share are Rs. 1125, 1875, and 2250 respectively.**

**Qu.6) A and B invest 20,000 and 30,000. After 2 months A invests Rs. 20,000 more and B also invests 20,000 more. After one year the total profit was Rs. 75,000. Find the share of B:**

**Sol.** Given: Capital invested by A = Rs. 20,000 and B = Rs. 30,000

According to the question,

After 2 Months their Capital –

A = 20,000 x 2 = Rs. 40,000

B = 30,000 x 2 = Rs. 60,000

Again after 10 months their capital (since, their time of investment is 1 year)

A = 40,000 x 10 = 4,00,000 (20,000 + 20,000)

B = 50,000 x 10 = 5,00,000 (30,000 + 20,000)

Total capital of A = 4,00,000 + 40,000 = 4,40,000

Total capital of B = 5,00,000 + 60,000 = 5,60,000

Ratio of capital of A and B = 4,40,000 : 5,60,000 = 44: 56 = 11: 14

B’s share = 14/(11 + 14) x 75000

= [14/ 25] x 75000

= Rs. 42000

**Ans. B’s share is Rs. 42,000.**

**Qu.7) The ratio of capitals of A: B: C is 3 : 4 : 2 and the ratio of their profit is 1 : 2 : 3. Find the ratio of their time :**

**Sol**. Given: Ratio of capitals of A : B: C = 3: 4: 2

Ratio of their profit = 1: 2: 3

As we know that, C x T = P

T = P/C

Therefore, Ratio of time of

A = 1/ 3 B = 2/ 4 C = 3/ 2

Multiplying them by 12

A = 1/3 x 12 = 4

B = 2/ 4 x 12 = 6

C = 3/ 2 x 12 = 18

A: B: C = 4: 6: 18 or 2: 3: 9

**Ans. Hence the required ratio is 2: 3: 9**

**Qu.8) A and B started a business with Rs. 3,50,000 and Rs. 1,40,000 respectively. A gets 20 % of profit for management and rest of the profit is divided in their capital ratio. If A gets Rs. 38000 more than B then find the total profit.**

**Sol**. Let the total profit be x

Now, A gets 20 % profit for managing business = ([20/ 100]. x) = x/ 5

Remaining profit = [ x – x/ 5] = 4x/ 5

Thereafter, Remaining profit will be distributed in the profit-sharing ratio I.e.,

350000: 140000 = 5:2

Therefore, A’s total share = [x/ 5 + (5/ 7. 4x/ 5)] = Rs. 27x/ 35 Eq.1

B’s share = 2/ 7 . 4x/ 5 = Rs. 8x/ 35 Eq.2

Therefore, difference eq.1 – eq.2 = 38000

27x/ 35 – 8x/ 35 = 38000

19x/ 35 = 38000

x = (38000 x 35)/ 19 = Rs. 70,000

**Ans. Therefore, total profit is Rs. 70,000**

**Qu.9) A, B and C started a business with a capital of Rs. 8 lac, 12 lac & 15 lac. A is a working partner & got 1/8 part in form of salary. If the total earning of A is Rs. 5200 then find the value of total profit.**

**Sol.** Given: Ratio of their Capitals = A : B: C = 8: 12: 15

Let us consider the total profit be 8 x 5 = 40

A’s salary = 1/8^{th} of profit = 1/ 8 x 40 = 5

Distributed Profit = 40 – 5 = 35

Now, A’s profit = 8 + 5 = 13

Total earning of A = 5200

13x = 5200

x = 5200/ 13 = 400

Therefore, Total Profit = 40 x = 40 x 400 = Rs. 16000

**Ans. The total profit is R. 16000**