A invested 25000 and B invested 75000 in a business and Ratio of time in which they invest is `7:4` .If the difference between their profit is 500 Rs , then what is the total profit ?

Options

A. A)1800
B. B)2000
C. C)1900
D. D)1700

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Determine the Investment Ratio
A invested ₹25,000 and B invested ₹75,000.

The investment ratio of A to B is:
\[ \text{Investment Ratio} = \frac{25000}{75000} = \frac{1}{3} \]

### Step 2: Combine with Time Ratio
The time ratio in which they invested is given as \(7:4\).

Now, we can combine the investment ratio and the time ratio to find the profit-sharing ratio.

### Step 3: Calculate the Profit Ratio
Let’s denote A's share of profit as \(P_A\) and B's share of profit as \(P_B\).

Using the investment and time ratios:
\[ P_A : P_B = \left(1 \times 7\right) : \left(3 \times 4\right) = 7 : 12 \]

### Step 4: Determine the Difference in Profit
According to the problem, the difference between their profits is ₹500.

Let’s denote the profit shares as:
\[ P_A = 7x \quad \text{and} \quad P_B = 12x \]

The difference in their profits can be expressed as:
\[ P_B - P_A = 12x - 7x = 5x \]
Given that this difference is ₹500:
\[ 5x = 500 \]

### Step 5: Solve for x
Now, we can solve for \(x\):
\[ x = \frac{500}{5} = 100 \]

### Step 6: Calculate Individual Profits
Now that we have \(x\), we can find the individual profits:
\[ P_A = 7x = 7 \times 100 = 700 \]
\[ P_B = 12x = 12 \times 100 = 1200 \]

### Step 7: Calculate Total Profit
The total profit is the sum of A's and B's profits:
\[ \text{Total Profit} = P_A + P_B = 700 + 1200 = 1900 \]

### Final Answer
Thus, the total profit is ₹1900.

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