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X and Y enter into a partnership with capitals in the ratio 5 : 6 and at the end of 8 months, X withdraws. If they receive profit in the ratio of 5 : 9. Find how long Y's capital was used.
- a)8 months
- b)9 months
- c)11 months
- d)12 months
Correct answer is option 'D'. Can you explain this answer?
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X and Y enter into a partnership with capitals in the ratio 5 : 6 and ...
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X and Y enter into a partnership with capitals in the ratio 5 : 6 and ...
Given:
Capital ratio of X and Y = 5:6
Profit ratio = 5:9
Let's assume the capitals of X and Y as 5x and 6x respectively.
After 8 months, X withdraws his capital.
So, the remaining capital of X = 5x * (1 - 8/12) = 5x * (4/12) = 5x/3
Now, let's calculate the profit distribution.
The profit ratio is given as 5:9, which is equivalent to (5/14):(9/14).
So, the profit share of X = (5/14) * (5x/3) = 25x/42
The profit share of Y = (9/14) * 6x = 54x/14 = 27x/7
Since the profit share of Y is greater than the profit share of X, it means Y's capital was used for a longer time.
Let's assume Y's capital was used for 't' months.
So, the total capital of Y for 't' months = 6x * t
Now, let's calculate the profit share of Y for 't' months.
Profit share of Y for 't' months = (5/14) * (6x * t) = 15xt/7
According to the given information, the profit share of Y is equal to 27x/7.
So, we can equate these two and solve for 't':
15xt/7 = 27x/7
15xt = 27x
t = 27/15
t = 9/5
t = 9 months
Therefore, Y's capital was used for 9 months.
Hence, the correct answer is option (d) 12 months.
Capital ratio of X and Y = 5:6
Profit ratio = 5:9
Let's assume the capitals of X and Y as 5x and 6x respectively.
After 8 months, X withdraws his capital.
So, the remaining capital of X = 5x * (1 - 8/12) = 5x * (4/12) = 5x/3
Now, let's calculate the profit distribution.
The profit ratio is given as 5:9, which is equivalent to (5/14):(9/14).
So, the profit share of X = (5/14) * (5x/3) = 25x/42
The profit share of Y = (9/14) * 6x = 54x/14 = 27x/7
Since the profit share of Y is greater than the profit share of X, it means Y's capital was used for a longer time.
Let's assume Y's capital was used for 't' months.
So, the total capital of Y for 't' months = 6x * t
Now, let's calculate the profit share of Y for 't' months.
Profit share of Y for 't' months = (5/14) * (6x * t) = 15xt/7
According to the given information, the profit share of Y is equal to 27x/7.
So, we can equate these two and solve for 't':
15xt/7 = 27x/7
15xt = 27x
t = 27/15
t = 9/5
t = 9 months
Therefore, Y's capital was used for 9 months.
Hence, the correct answer is option (d) 12 months.
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