Question : A and B started a business partnership by investing in a ratio of 3 : 8. C joined them after 4 months with an amount equal to $\frac{3}{4}$th of B. What was their profit (in Rs.) at the end of the year if C got Rs. 24,000 as his share?
Option 1: 1,20,000
Option 2: 1,50,000
Option 3: 90,000
Option 4: 1,80,000
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Correct Answer: 90,000
Solution :
Ratio of investment = 3 : 8
Let the investment by A = 3$x$ and investment by B = 8$x$
⇒ Investment by C = 8$x$ × $\frac{3}{4}$ = 6$x$
Ratio in which the profit is shared
= (capital of A × time period of A) : (capital of B × time period of B) : (capital of C × time period of C)
= (3$x$ × 12) : (8$x$ × 12) : (6$x$ × 8)
= 3 : 8 : 4
Since share of C = Rs. 24000
⇒ 24000 = $\frac{4}{3+8+4}$ × total profit
⇒ Total profit = $\frac{24000×15}{4}$ = Rs. 90000
Hence, the correct answer is 90,000.
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