Hutch and Essar entered into a partnership just 5 months ago. The ratio of profit claimed by Hutch Essar is 6:17. If Essar hand just started his business 12 months ago with Rs. 1275, what is the amount contributed by Hutuch?

Options

A. Rs. 980
B. Rs. 1080
C. Rs. 1200
D. Rs. 998

Answer

To solve the problem step by step, let's break it down clearly.

### Step 1: Understand the Given Information
- Hutch and Essar entered into a partnership 5 months ago.
- The profit ratio claimed by Hutch and Essar is 6:17.
- Essar started his business 12 months ago with Rs. 1275.
- We need to find the amount contributed by Hutch.

### Step 2: Set Up the Variables
Let the amount contributed by Hutch be \( X \) rupees.

### Step 3: Calculate the Time Periods
- Essar has been in the business for 12 months.
- Hutch has been in the business for 5 months.

### Step 4: Set Up the Profit Sharing Equation
The profit sharing ratio is based on the amount invested and the time for which it is invested. Therefore, we can express the profit ratio as:

\[ \frac{\text{Profit of Hutch}}{\text{Profit of Essar}} = \frac{X \times 5}{1275 \times 12} \]

Given that the profit ratio is \( \frac{6}{17} \), we can set up the equation:

\[ \frac{X \times 5}{1275 \times 12} = \frac{6}{17} \]

### Step 5: Cross-Multiply to Solve for \( X \)
Cross-multiplying gives us:

\[ 17 \times (X \times 5) = 6 \times (1275 \times 12) \]

### Step 6: Simplify the Equation
Calculating the right side:

\[ 6 \times (1275 \times 12) = 6 \times 15300 = 91800 \]

Now the equation becomes:

\[ 85X = 91800 \]

### Step 7: Solve for \( X \)
Now, divide both sides by 85:

\[ X = \frac{91800}{85} \]

Calculating the value:

\[ X = 1080 \]

### Step 8: Conclusion
The amount contributed by Hutch is Rs. 1080.

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