Dev and Deepak start a business in partnership. Dev invested 25% more capital than Deepak but he invested for 4 months less than that by Deepak. If the profit share of Deepak is Rs.4000, which is Rs.1000, more than that of Dev, then find the time of investment of Dev.

Correct Answer: 6 months

Step-by-step Explanation:

1. Understanding the ratio of profits:

The total profit share of Deepak is given as Rs. 4000.

The profit share of Deepak is Rs. 1000 more than that of Dev.

Therefore, the profit share of Dev = Rs. 4000 - Rs. 1000 = Rs. 3000.

Now, let us find the ratio of profit share of Dev to Deepak:

$\frac{\text{Profit of Dev}}{\text{Profit of Deepak}}=\frac{3000}{4000}=\frac{3}{4}$

2. Setting up the investments and time periods:

Let the capital invested by Deepak be C_Deepak = 100.

Dev invested 25% more capital than Deepak, so:

C_Dev = 100 + 25 = 125.

The ratio of their capitals is:

$\frac{C_{\text{Dev}}}{C_{\text{Deepak}}}=\frac{125}{100}=\frac{5}{4}$

Let the time for which Deepak invested be T months.

Since Dev invested for 4 months less than Deepak, the time of investment for Dev is (T - 4) months.

3. Relating profit ratio to investment ratio:

Profit share is proportional to the product of capital and time period of investment.

$\frac{\text{Profit of Dev}}{\text{Profit of Deepak}}=\frac{C_{\text{Dev}}\times T_{\text{Dev}}}{C_{\text{Deepak}}\times T_{\text{Deepak}}}$

Substitute the known values into the ratio equation:

$\frac{3}{4}=\frac{5\times (T-4)}{4\times T}$

Multiplying both sides by 4:

$3=\frac{5(T-4)}{T}$

Cross-multiplying to solve for T:

$3T=5T-20$

$2T=20$

$T=10\text{months}$

4. Finding the investment period for Dev:

Deepak invested for T = 10 months.

Dev invested for (T - 4) months = 10 - 4 = 6 months.