Question : A started a business with a capital of Rs. 54,000 and admitted B and C after 4 months and 6 months, respectively. At the end of the year, the profit was divided among the three in the ratio 1 : 4 : 5. What is the sum (in Rs.) of the capital invested by B and C?
Option 1: 8,64,000
Option 2: 8,40,060
Option 3: 8,46,000
Option 4: 8,60,400
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Correct Answer: 8,64,000
Solution :
In a business partnership, the share of profit is proportional to the product of the capital invested and the time for which the capital is invested.
Let the capital invested by B and C as $x$ and $y$ respectively.
The time for B to invest their capital = 12 – 4 = 8 months
The time for C to invest their capital = 12 – 6 = 6 months
According to the question,
$⇒\frac{54000 \times 12}{x \times 8}=\frac{1}{4}$
$⇒x=54000\times 6$
$⇒x=324000$
And,
$⇒\frac{54000 \times 12}{y \times 6}=\frac{1}{5}$
$⇒y=54000\times 10$
$⇒y=540000$
The sum of the capital invested by B and C = 324000 + 540000 = Rs. 8,64,000
Hence, the correct answer is 8,64,000.
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