Question : A and B started a business with Rs. 15000 and Rs. 30000, respectively. If A and B share profit in the ratio of 1 : 5 respectively, then what is the ratio of the time period of investment for A and B respectively?
Option 1: 1 : 2
Option 2: 2 : 5
Option 3: 2 : 3
Option 4: 2 : 7
Correct Answer: 2 : 5
Solution :
In a business, the share of profit is directly proportional to the product of the capital invested and the time period of investment.
The time period of investment for A is $p$ and the time period of investment for B is $q$.
Given that the ratio of the capital invested by A and B is 15000 : 30000 or 1 : 2, and the ratio of their share in profit is 1 : 5.
$⇒\frac{\text{Investment by A × p}}{\text{Investment by B × q}}=\frac{\text{Share of profit of A }}{\text{Share of profit of B }}$
$⇒\frac{\text{1 × p}}{\text{2 × q}}=\frac{\text{1 }}{\text{5}}$
$\therefore\frac{\text{ p}}{\text{q}}=\frac{\text{2}}{\text{5}}$
Hence, the correct answer is 2 : 5.
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