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X and Y are partners in a business. They invest in the ratio 5 : 6, at the end of 8 months X withdraws his capital. If they receive profits in the ratio of 5 : 9. Find how long Y's investment was used ?
  • a)
    12 months
  • b)
    10 months
  • c)
    15 months
  • d)
    14 months
Correct answer is option 'A'. Can you explain this answer?
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X and Y are partners in a business. They invest in the ratio 5 : 6, at...
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X and Y are partners in a business. They invest in the ratio 5 : 6, at...
Given:
- X and Y are partners in a business.
- They invest in the ratio 5:6.
- X withdraws his capital at the end of 8 months.
- They receive profits in the ratio 5:9.

To find:
- The duration for which Y's investment was used.

Solution:
Let's assume that X invested 5x and Y invested 6x.

Investment Ratio:
X's investment = 5x
Y's investment = 6x

Profit Sharing Ratio:
X's profit share = 5
Y's profit share = 9

Calculation:
Since X withdraws his capital after 8 months, his investment is used for 8 months. Therefore, the ratio of their investments for the remaining duration is:

X's investment = 5x (for 8 months)
Y's investment = 6x (for the remaining months)

The profit sharing ratio is given as 5:9, which means that the ratio of their investments is equal to the ratio of their profit shares. So, we can set up the following equation:

5x/8 = 5/9

Cross-multiplying:
45x = 40

Dividing by 45:
x = 40/45
x = 8/9

Calculating Y's investment:
Y's investment = 6x
Y's investment = 6 * (8/9)
Y's investment = 48/9
Y's investment = 16/3

Calculating the duration for which Y's investment was used:
Since X's investment was used for 8 months, Y's investment was used for the remaining duration:

Total duration - X's duration = Y's duration
12 months - 8 months = 4 months

Therefore, Y's investment was used for 4 months.

Conclusion:
The duration for which Y's investment was used is 4 months, which is equivalent to option A.
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X and Y are partners in a business. They invest in the ratio 5 : 6, at the end of 8 months X withdraws his capital. If they receive profits in the ratio of 5 : 9. Find how long Y's investment was used ?a)12 monthsb)10 monthsc)15 monthsd)14 monthsCorrect answer is option 'A'. Can you explain this answer?
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