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A, B, C started a business with their investments in the ratio 1 : 3 : 5. After 4 months, A invested the same amount as before and B as well as C withdrew half of their investments. The ratio of their profits at the end of the year is ?
  • a)
    4 : 3 : 5
  • b)
    5 : 6 : 10
  • c)
    6 : 5 : 10
  • d)
    10 : 5 : 6
Correct answer is option 'B'. Can you explain this answer?
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A, B, C started a business with their investments in the ratio 1 : 3 :...
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A, B, C started a business with their investments in the ratio 1 : 3 :...
Given:
- Investments ratio of A, B, C = 1:3:5
- After 4 months:
- A invests the same amount as before
- B and C withdraw half of their investments

To find: Ratio of their profits at the end of the year

Solution:
Let's assume the initial investments of A, B, and C as x, 3x, and 5x respectively.

Investments:
- Initial investments:
- A = x
- B = 3x
- C = 5x

- After 4 months:
- A invests the same amount as before = x
- B withdraws half of the investment = 3x/2
- C withdraws half of the investment = 5x/2

Effective Investments:
- After 4 months:
- A = x + x = 2x
- B = 3x - 3x/2 = 3x/2
- C = 5x - 5x/2 = 5x/2

Profit Sharing:
- The profit of a business is usually shared in proportion to the investments made by the partners.

- The ratio of their profits will be equal to the ratio of their effective investments.

Ratio of Profits:
- Ratio of their profits at the end of the year:
- A : B : C = 2x : 3x/2 : 5x/2

Simplifying the Ratio:
- To simplify the ratio, we multiply each part by the least common multiple (LCM) of the denominators, which is 2.
- A : B : C = 2x * 2 : 3x/2 * 2 : 5x/2 * 2
- A : B : C = 4x : 3x : 5x
- A : B : C = 4 : 3 : 5

Answer:
The ratio of their profits at the end of the year is 4 : 3 : 5 (option B).
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A, B, C started a business with their investments in the ratio 1 : 3 : 5. After 4 months, A invested the same amount as before and B as well as C withdrew half of their investments. The ratio of their profits at the end of the year is ?a)4 : 3 : 5b)5 : 6 : 10c)6 : 5 : 10d)10 : 5 : 6Correct answer is option 'B'. Can you explain this answer?
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