U and V started a business by investing amounts Rs 184000 and Rs 224000respectively. If U’s share in the profit received at the end of year is Rs 20700,then what will be the total profit (in Rs)earned by them together?

Options

A. 43200
B. 45900
C. 52300
D. 56400

Answer

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

### Step 1: Determine the investment ratio of U and V
U's investment = Rs 184,000
V's investment = Rs 224,000

To find the ratio of their investments, we can express it as:
\[ \text{Ratio of U to V} = \frac{184000}{224000} \]

### Step 2: Simplify the investment ratio
We can simplify the ratio:
\[ \text{Ratio} = \frac{184}{224} = \frac{23}{28} \]
Thus, the investment ratio of U to V is 23:28.

### Step 3: Find the total parts in the ratio
The total parts in the ratio = 23 + 28 = 51 parts.

### Step 4: Determine U's share in the profit
From the problem, we know that U's share in the profit is Rs 20,700. Since U's share corresponds to 23 parts of the total profit, we can set up the equation:
\[ \text{U's share} = \frac{23}{51} \times \text{Total Profit} \]
Let Total Profit be \( P \):
\[ 20700 = \frac{23}{51} \times P \]

### Step 5: Solve for Total Profit (P)
To find \( P \), we can rearrange the equation:
\[ P = 20700 \times \frac{51}{23} \]

### Step 6: Calculate the Total Profit
Now, we can compute \( P \):
\[ P = 20700 \times \frac{51}{23} = 20700 \times 2.217391304347826 = 45900 \]

### Conclusion
The total profit earned by U and V together is Rs 45,900.