Question
Download Solution PDFIn a partnership business, A invests 1 /6th of the capital for 1/6 of the total time, B invests 1/4th of the capital for 1/4 of the total time and C, the rest of the capital for the whole time. Find the share of B, out of a profit of Rs. 1940.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Investment by A = 1/6 of the capital for 1/6 of the time
Investment by B = 1/4 of the capital for 1/4 of the time
Investment by C = Rest of the capital for the whole time
Total profit = ₹1940
Formula used:
Share of profit is proportional to the product of capital and time invested.
Calculation:
Contribution of A = (1/6) × (1/6) = 1/36
Contribution of B = (1/4) × (1/4) = 1/16
Contribution of C = (1 - 1/6 - 1/4) × 1 = 7/12 × 1 = 7/12
Now, ratio of their contributions:
A : B : C = 1/36 : 1/16 : 7/12
To simplify, find the LCM of the denominators (36, 16, 12) = 144
Now, convert the ratios:
A : B : C = 4/144 : 9/144 : 84/144
⇒ A : B : C = 4 : 9 : 84
Total parts = 4 + 9 + 84 = 97
B's share = (9/97) × 1940
⇒ B's share = ₹180
∴ B's share of the profit is ₹180.
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