Suresh started a business by investing a certain amount of money. Rakesh joined him after four months by investing Rs.50000. If after one year Suresh and Rakesh share the profit in the ratio of 10:8, how much capital did Suresh invest?

41666.7

In a business partnership, the profit is shared in the ratio of the product of the capital invested and the time period for which it was invested:

$\text{Profit Ratio} = (\text{Investment}_1 \times \text{Time}_1) : (\text{Investment}_2 \times \text{Time}_2)$

Let Suresh's capital investment be $X$.

Step 1: Identify the time periods and investments

• Suresh: Invested Rs. $X$ for the entire year ($12\text{ months}$).
• Rakesh: Invested Rs. $50000$ after 4 months, meaning his money was invested for $12 - 4 = 8\text{ months}$.

Step 2: Set up the ratio equation

$\frac{\text{Suresh's Profit}}{\text{Rakesh's Profit}} = \frac{X \times 12}{50000 \times 8}$

Given that the profit ratio is $10:8$:

$\frac{10}{8} = \frac{12X}{400000}$

Step 3: Solve for $X$

Cross-multiplying to solve the equation:

$12X \times 8 = 10 \times 400000$

$96X = 4000000$

$X = \frac{4000000}{96}$

$X \approx 41666.7$