Out of a total profit of Rs 19,600, B received Rs 10,000 as his share. If A invested Rs 8,000 for 6 months while B invested his amount for 5 months, then what is the amount invested by B?
Question
Out of a total profit of Rs 19,600, B received Rs 10,000 as his share. If A invested Rs 8,000 for 6 months while B invested his amount for 5 months, then what is the amount invested by B?
Solution
The problem involves the concept of ratio and proportion. Here, the profit shared is directly proportional to the product of the money invested and the time period of investment.
Let's denote:
- The amount invested by A as 'Pa' = Rs 8,000
- The time period of A's investment as 'Ta' = 6 months
- The amount invested by B as 'Pb' (which we need to find)
- The time period of B's investment as 'Tb' = 5 months
The profit of A is the total profit minus the profit of B, which is Rs 19,600 - Rs 10,000 = Rs 9,600.
The ratio of A's profit to B's profit is therefore Rs 9,600 / Rs 10,000 = 0.96.
According to the problem, this ratio is equal to the ratio of the product of the money invested and the time period of investment for A and B. So we can write:
(Pa * Ta) / (Pb * Tb) = 0.96
Substituting the known values:
(8000 * 6) / (Pb * 5) = 0.96
Solving this equation for Pb gives:
Pb = (8000 * 6) / (0.96 * 5)
Pb = Rs 10,000
So, B invested Rs 10,000.
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