In a monthly unit test, the marks scored by Bunny and Sunny are in the ratio of ` 10 : 7` and those scored by Bharat and Sunny are in the ratio of ` 8 : 9`. If Bharat 112 marks, then find the marks scored by Bunny.

Options

A. 170
B. 190
C. 200
D. 180

Explanation

To solve the problem, we will follow these steps:

### Step 1: Define the Variables
Let the marks scored by Bunny be \( B \), the marks scored by Sunny be \( S \), and the marks scored by Bharat be \( R \).

### Step 2: Set Up Ratios
From the problem, we know:
1. The ratio of marks scored by Bunny and Sunny is \( 10:7 \).
\[ \frac{B}{S} = \frac{10}{7} \]
This can be rewritten as:
\[ B = \frac{10}{7} S \quad \text{(1)} \]

2. The ratio of marks scored by Bharat and Sunny is \( 8:9 \).
\[ \frac{R}{S} = \frac{8}{9} \]
This can be rewritten as:
\[ R = \frac{8}{9} S \quad \text{(2)} \]

### Step 3: Substitute the Known Value
We know that Bharat scored \( R = 112 \) marks. Using equation (2):
\[ 112 = \frac{8}{9} S \]

### Step 4: Solve for S
To find \( S \), we can rearrange the equation:
\[ S = 112 \times \frac{9}{8} \]
Calculating this gives:
\[ S = 112 \times 1.125 = 126 \]

### Step 5: Substitute S Back to Find B
Now that we have \( S = 126 \), we can substitute this value back into equation (1) to find \( B \):
\[ B = \frac{10}{7} \times 126 \]
Calculating this gives:
\[ B = 10 \times 18 = 180 \]

### Final Answer
Thus, the marks scored by Bunny are \( \boxed{180} \).

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