In a partnership business, Q’s capital was half of P’s if after 8 months,Q withdrew half of his capital and after 2 months more P withdrew 1/4th of his capital, then the profit ratio of P and Q after 1 year will beOptions7 : 29 : 237 : 523 : 10
Question
In a partnership business, Q’s capital was half of P’s if after 8 months,Q withdrew half of his capital and after 2 months more P withdrew 1/4th of his capital, then the profit ratio of P and Q after 1 year will beOptions7 : 29 : 237 : 523 : 10
Solution
The problem is about the distribution of profit in a partnership based on the capital contribution and the time for which the capital was invested.
Let's denote P's capital as 2x (since Q's capital is half of P's, we denote Q's capital as x).
- For the first 8 months, P's capital is 2x and Q's capital is x.
- For the next 2 months, P's capital is still 2x but Q's capital is halved to 0.5x.
- For the last 2 months of the year, P's capital is reduced to 1.75x (since he withdrew 1/4th) and Q's capital remains at 0.5x.
The profit share is proportional to the product of the capital invested and the time for which it was invested.
So, P's share of the profit = (2x8 months) + (2x2 months) + (1.75x*2 months) = 16x + 4x + 3.5x = 23.5x
And Q's share of the profit = (x8 months) + (0.5x2 months) + (0.5x*2 months) = 8x + x + x = 10x
Therefore, the ratio of P's profit to Q's profit = 23.5x : 10x = 47 : 20
So, none of the given options match the calculated ratio.
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