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A and B started a business by investing money in the ratio of 4 : 5. After 9 months C joined them by investing thrice the amount as A. At the end of the year, a profit of Rs.14400 is earned. What will be share of B?
- a)1200
- b)2400
- c)6000
- d)5400
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A and B started a business by investing money in the ratio of 4 : 5. A...
Let, A’s investment = 4x
B’s investment = 5x
∴ C’s investment = 3 × 4x = 12x
∴ Weighted ratio of investment of A, B, C = 4x × 12 : 5x × 12 : 12x × (12 - 9)
⇒ 48x : 60x : 36x
⇒ 4 : 5 : 3
∴ B’s share in this profit = (5/12) × 14400 = 6000
B’s investment = 5x
∴ C’s investment = 3 × 4x = 12x
∴ Weighted ratio of investment of A, B, C = 4x × 12 : 5x × 12 : 12x × (12 - 9)
⇒ 48x : 60x : 36x
⇒ 4 : 5 : 3
∴ B’s share in this profit = (5/12) × 14400 = 6000
Most Upvoted Answer
A and B started a business by investing money in the ratio of 4 : 5. A...
Given:
A and B invested money in the ratio of 4:5.
C joined after 9 months by investing thrice the amount as A.
Total profit at the end of the year is Rs. 14400.
To find:
Share of B in the profit.
Solution:
Let's assume the capital invested by A and B as 4x and 5x respectively.
Investment Ratio:
A:B = 4:5
Profit Sharing Ratio:
Since A and B invested for the whole year, their profit sharing ratio will be the same as their investment ratio, which is 4:5.
Capital of C:
C joined after 9 months, which means C invested for only 3 months.
Let's assume the capital invested by A as 'a'.
Therefore, the capital invested by C = 3 * (Capital invested by A) = 3a.
Profit Sharing Ratio for C:
Since C invested for only 3 months, the profit sharing ratio for C will be 3:12 (3 months for C and 9 months for A and B).
To make the ratio in terms of a common multiple, we can simplify it further.
The ratio becomes 1:4.
Profit Distribution:
Total profit = Rs. 14400
Share of A:
Share of A = (Profit sharing ratio of A / Total of profit sharing ratios) * Total profit
= (4 / (4 + 5 + 1)) * 14400
= (4 / 10) * 14400
= 5760
Share of B:
Share of B = (Profit sharing ratio of B / Total of profit sharing ratios) * Total profit
= (5 / (4 + 5 + 1)) * 14400
= (5 / 10) * 14400
= 7200
Share of C:
Share of C = (Profit sharing ratio of C / Total of profit sharing ratios) * Total profit
= (1 / (4 + 5 + 1)) * 14400
= (1 / 10) * 14400
= 1440
Final Answer:
Therefore, the share of B in the profit is Rs. 7200, which is option C.
A and B invested money in the ratio of 4:5.
C joined after 9 months by investing thrice the amount as A.
Total profit at the end of the year is Rs. 14400.
To find:
Share of B in the profit.
Solution:
Let's assume the capital invested by A and B as 4x and 5x respectively.
Investment Ratio:
A:B = 4:5
Profit Sharing Ratio:
Since A and B invested for the whole year, their profit sharing ratio will be the same as their investment ratio, which is 4:5.
Capital of C:
C joined after 9 months, which means C invested for only 3 months.
Let's assume the capital invested by A as 'a'.
Therefore, the capital invested by C = 3 * (Capital invested by A) = 3a.
Profit Sharing Ratio for C:
Since C invested for only 3 months, the profit sharing ratio for C will be 3:12 (3 months for C and 9 months for A and B).
To make the ratio in terms of a common multiple, we can simplify it further.
The ratio becomes 1:4.
Profit Distribution:
Total profit = Rs. 14400
Share of A:
Share of A = (Profit sharing ratio of A / Total of profit sharing ratios) * Total profit
= (4 / (4 + 5 + 1)) * 14400
= (4 / 10) * 14400
= 5760
Share of B:
Share of B = (Profit sharing ratio of B / Total of profit sharing ratios) * Total profit
= (5 / (4 + 5 + 1)) * 14400
= (5 / 10) * 14400
= 7200
Share of C:
Share of C = (Profit sharing ratio of C / Total of profit sharing ratios) * Total profit
= (1 / (4 + 5 + 1)) * 14400
= (1 / 10) * 14400
= 1440
Final Answer:
Therefore, the share of B in the profit is Rs. 7200, which is option C.
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