Srikant and Vividh started a business investing amounts of X 185000 and X 225000, respectively. If Vividh's share in the profit earned by them is X 9000, what is the total profit earned by them together ?

Options

A. 17400
B. 16400
C. 16800
D. 17800

Answer

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

### Step 1: Determine the investment ratio
Srikant's investment = ₹185,000
Vividh's investment = ₹225,000

To find the ratio of their investments, we can express it as:
\[ \text{Ratio} = \frac{185000}{225000} \]

### Step 2: Simplify the ratio
We can simplify the ratio by dividing both amounts by 1000:
\[ \text{Ratio} = \frac{185}{225} \]

Next, we can simplify this further by dividing both numbers by 5:
\[ \frac{185 \div 5}{225 \div 5} = \frac{37}{45} \]

So, the investment ratio of Srikant to Vividh is 37:45.

### Step 3: Set up the profit-sharing formula
Let Srikant's share of profit be represented as \( 37X \) and Vividh's share of profit as \( 45X \).

### Step 4: Use Vividh's profit share to find \( X \)
According to the problem, Vividh's share in the profit is ₹9,000:
\[ 45X = 9000 \]

### Step 5: Solve for \( X \)
To find \( X \), divide both sides by 45:
\[ X = \frac{9000}{45} \]

Calculating this gives:
\[ X = 200 \]

### Step 6: Calculate the total profit
Now that we have \( X \), we can find the total profit:
\[ \text{Total Profit} = Srikant's share + Vividh's share \]
\[ = 37X + 45X \]
\[ = 82X \]

Substituting \( X = 200 \):
\[ \text{Total Profit} = 82 \times 200 \]
\[ = 16400 \]

### Final Answer
The total profit earned by them together is ₹16,400.

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