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

Options

A. ₹ 980
B. ₹ 1080
C. ₹ 1200
D. ₹ 998

Answer

To solve the problem step by step, we need to understand the partnership between Hutch and Essar, their investment amounts, and how long they have been in the business.

### Step 1: Understand the time of investment
Essar has been in the business for 12 months, while Hutch has only been in for 5 months. This means that the profit distribution will be based on the amount of money invested multiplied by the time each partner has been in the business.

### Step 2: Define the variables
Let the amount contributed by Hutch be \( x \) rupees. Essar's investment is given as ₹1275.

### Step 3: Calculate the effective investment
- Hutch's effective investment for 5 months is \( 5x \).
- Essar's effective investment for 12 months is \( 1275 \times 12 = 15300 \).

### Step 4: Set up the ratio of profits
The ratio of profits claimed by Hutch and Essar is given as 6:17. Therefore, we can set up the equation:
\[ \frac{5x}{15300} = \frac{6}{17} \]

### Step 5: Cross-multiply to solve for \( x \)
Cross-multiplying gives us:
\[ 5x \cdot 17 = 6 \cdot 15300 \]
\[ 85x = 91800 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 85 to find \( x \):
\[ x = \frac{91800}{85} = 1080 \]

### Conclusion
The amount contributed by Hutch is ₹1080.

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