Ex. No. 1.2
1. Ajay, Atul and Anil started a business in a partnership by increasing Rs. 12,000, Rs. 18,000 and Rs. 30,000 respectively. At the end of the year, they earned a profit of Rs. 15,200 in the business. Find the share of each in the profit.
Solution:
Ratio of their investments = 12,000 : 18,000 : 30,000 = 12 : 18 : 30 = 2 : 3 : 5
Total ratio parts = $2 + 3 + 5 = 10$
Total profit = Rs. 15,200
Ajay's share = $\frac{2}{10} \times 15,200 = \text{Rs. } 3,040$
Atul's share = $\frac{3}{10} \times 15,200 = \text{Rs. } 4,560$
Anil's share = $\frac{5}{10} \times 15,200 = \text{Rs. } 7,600$
2. Raghu, Madhu and Ramu started a business in a partnership by investing Rs. 60,000, Rs. 40,000 and Rs. 75,000 respectively. At the end of the year they found that they have incurred a loss of Rs. 24,500. Find how much loss each one had to bear.
Solution:
Ratio of their investments = 60,000 : 40,000 : 75,000 = 60 : 40 : 75 = 12 : 8 : 15
Total ratio parts = $12 + 8 + 15 = 35$
Total loss = Rs. 24,500
Raghu's loss = $\frac{12}{35} \times 24,500 = 12 \times 700 = \text{Rs. } 8,400$
Madhu's loss = $\frac{8}{35} \times 24,500 = 8 \times 700 = \text{Rs. } 5,600$
Ramu's loss = $\frac{15}{35} \times 24,500 = 15 \times 700 = \text{Rs. } 10,500$
3. A, B and C are in the partnership. A's capital was Rs. 65,000 and C's capital was Rs. 50,000. The total profit is Rs. 38,000; out of which B's profit was Rs. 15,000. What was B's capital?
Solution:
Total Profit = Rs. 38,000
B's Profit = Rs. 15,000
Remaining profit for A and C = $38,000 - 15,000 = \text{Rs. } 23,000$The ratio of A's capital to C's capital is 65,000 : 50,000 = 13 : 10.
A's profit = $\frac{13}{23} \times 23,000 = \text{Rs. } 13,000$
C's profit = $\frac{10}{23} \times 23,000 = \text{Rs. } 10,000$The ratio of profits of A : B : C = 13,000 : 15,000 : 10,000 = 13 : 15 : 10.
Since profit ratio is equal to capital ratio (assuming equal time periods), B's capital corresponds to the ratio part of 15.
Comparing C and B: $\frac{\text{C's Capital}}{10} = \frac{\text{B's Capital}}{15}$
$\frac{50,000}{10} = \frac{\text{B's Capital}}{15}$
B's Capital = $5,000 \times 15 = \text{Rs. } 75,000$
4. Paul and Qasim started a business with equal amount of capital. After 8 months Paul withdrew his amount and Raja entered in the business with same of capital. At the end of the year they found that they have incurred a loss of Rs. 24, 500. Find how much loss each one had to bear.
Solution:
Let the initial equal capital be $x$.
Paul's investment equivalent = $x \times 8 \text{ months} = 8x$
Qasim's investment equivalent = $x \times 12 \text{ months} = 12x$
Raja's investment equivalent = $x \times 4 \text{ months} = 4x$ (since he entered after 8 months)Ratio of their shares = $8x : 12x : 4x = 8 : 12 : 4 = 2 : 3 : 1$
Total ratio parts = $2 + 3 + 1 = 6$
Total Loss = Rs. 24,500Paul's loss = $\frac{2}{6} \times 24,500 = \text{Rs. } 8,166.67$
Qasim's loss = $\frac{3}{6} \times 24,500 = \text{Rs. } 12,250$
Raja's loss = $\frac{1}{6} \times 24,500 = \text{Rs. } 4,083.33$
5. Amit and Rohit started a business by investing Rs. 20,000 each. After 3 months Amit withdrew Rs. 5000 and Rohit put in the same amount additionally. How should a profit of Rs. 12,800 be divided between them at the end of the year?
Solution:
Amit's equivalent capital for 1 year = $(20,000 \times 3) + (15,000 \times 9) = 60,000 + 135,000 = 195,000$
Rohit's equivalent capital for 1 year = $(20,000 \times 3) + (25,000 \times 9) = 60,000 + 225,000 = 285,000$
Ratio of their profit shares = 195,000 : 285,000 = 195 : 285 = 39 : 57 = 13 : 19
Total ratio parts = $13 + 19 = 32$
Total Profit = Rs. 12,800Amit's share = $\frac{13}{32} \times 12,800 = 13 \times 400 = \text{Rs. } 5,200$
Rohit's share = $\frac{19}{32} \times 12,800 = 19 \times 400 = \text{Rs. } 7,600$
6. John and Mathew started a business with their capitals in the ratio 8:5. After 8 months John added 25% of his earlier capital as further investments. At the same time Mathew withdrew 20% of his earlier capital. At the end of the year they earned Rs. 52000 as profit. How should they divide it between them?
Solution:
Let initial capitals be $8x$ and $5x$.
John's capital for first 8 months = $8x$
John's new capital for next 4 months = $8x + 0.25(8x) = 8x + 2x = 10x$
John's equivalent capital = $(8x \times 8) + (10x \times 4) = 64x + 40x = 104x$Mathew's capital for first 8 months = $5x$
Mathew's new capital for next 4 months = $5x - 0.20(5x) = 5x - 1x = 4x$
Mathew's equivalent capital = $(5x \times 8) + (4x \times 4) = 40x + 16x = 56x$Ratio of shares = $104x : 56x = 104 : 56 = 13 : 7$
Total ratio parts = $13 + 7 = 20$
Total Profit = Rs. 52,000John's share = $\frac{13}{20} \times 52,000 = 13 \times 2,600 = \text{Rs. } 33,800$
Mathew's share = $\frac{7}{20} \times 52,000 = 7 \times 2,600 = \text{Rs. } 18,200$
7. Ramesh, Vivek and Sunil started a business by investing the capitals in the ratio 4:5:6. After 3 months Vivek removed all his capital and after 6 months Sunil removed all his capital from the business. At the end of the year Ramesh received Rs. 6400 as profit. Find the profit earned by Vivek and Sunil.
Solution:
Let the capitals be $4x$, $5x$, and $6x$.
Ramesh's investment equivalent = $4x \times 12 = 48x$
Vivek's investment equivalent = $5x \times 3 = 15x$
Sunil's investment equivalent = $6x \times 6 = 36x$Ratio of profit sharing = $48x : 15x : 36x = 48 : 15 : 36 = 16 : 5 : 12$
Ramesh's profit = Rs. 6,400.
Therefore, 16 parts = Rs. 6,400 $\Rightarrow 1 \text{ part} = \text{Rs. } 400$Vivek's profit (5 parts) = $5 \times 400 = \text{Rs. } 2,000$
Sunil's profit (12 parts) = $12 \times 400 = \text{Rs. } 4,800$
8. Mr. Natarajan and Mr. Gopalan are partners in a company having capitals in the ratio 4:5 and profits received by them are in the ratio 5:4. If Gopalan invested capital in the company for 16 months, how long was Natrajan’s investment in the company?
Solution:
Let Natarajan's capital be $4x$ and Gopalan's be $5x$.
Let Natarajan's investment time be $T$ months. Gopalan's time = 16 months.Ratio of profits = $\frac{\text{Capital} \times \text{Time}}{\text{Capital} \times \text{Time}}$
$\frac{4x \times T}{5x \times 16} = \frac{5}{4}$
$\frac{4T}{80} = \frac{5}{4}$
$\frac{T}{20} = \frac{5}{4}$
$T = \frac{5 \times 20}{4} = 25 \text{ months}$
Natarajan's investment was in the company for 25 months.
9. Anita and Nameeta are partners in the business for some years. Their capitals are Rs. 3,00,000 and Rs. 2,00,000 respectively. Yogeeta wants to join the business with the capital of Rs. 4,00,000. They agree that the goodwill will be considered as two times the average of last three years profit. The profit of last three years are Rs. 60,000, Rs. 70,000 and Rs. 50,000 respectively. What are the amounts to be paid by Yogeeta and Anita and Nameeta as goodwill?
Solution:
Average profit = $\frac{60,000 + 70,000 + 50,000}{3} = \frac{180,000}{3} = \text{Rs. } 60,000$
Total Goodwill of the firm = $2 \times 60,000 = \text{Rs. } 120,000$
Old ratio (Anita : Nameeta based on capital) = 3,00,000 : 2,00,000 = 3 : 2
New ratio (Anita : Nameeta : Yogeeta) = 3 : 2 : 4
Total new ratio parts = $3 + 2 + 4 = 9$Yogeeta's share of goodwill to bring in = $\frac{4}{9} \times 120,000 = \text{Rs. } 53,333.33$
This goodwill premium is distributed to the old partners in their sacrificing ratio. Since the new ratio is proportional to their old capital, the sacrificing ratio remains the same as their old ratio (3:2).
Anita receives = $\frac{3}{5} \times 53,333.33 = \text{Rs. } 32,000$
Nameeta receives = $\frac{2}{5} \times 53,333.33 = \text{Rs. } 21,333.33$
10. A, B and C are three partners with their capitals in the ratio 4:3:3. They decide to dissolve the partnership. The assets of the company are sold for Rs. 4,00,000 and liabilities (other than capital) of Rs. 60,000. They incur realisation expenses of Rs. 4,000. What is the amount that each partner gets as final settlement after dissolution?
Solution:
Amount realized from assets = Rs. 4,00,000
Less: Outside liabilities paid = Rs. 60,000
Less: Realisation expenses paid = Rs. 4,000Net cash available for distribution to partners = $4,00,000 - 60,000 - 4,000 = \text{Rs. } 3,36,000$
Since specific capital amounts are not provided, the net available cash is distributed in their profit-sharing / capital ratio of 4:3:3.
Total ratio parts = $4 + 3 + 3 = 10$
Amount A gets = $\frac{4}{10} \times 3,36,000 = \text{Rs. } 1,34,400$
Amount B gets = $\frac{3}{10} \times 3,36,000 = \text{Rs. } 1,00,800$
Amount C gets = $\frac{3}{10} \times 3,36,000 = \text{Rs. } 1,00,800$
