Weights of two friends A and B are in the ratio of 7 : 8. A’s weight increases by 10% and the total weight of A and B increase by 20%. What is the percentage increase in the B’s weight?

Options

A. 28.75
B. 11.55
C. 32.85
D. 24.25

Explanation

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

### Step 1: Define the weights of A and B
Let the weights of A and B be represented as:
- Weight of A = 7x
- Weight of B = 8x

### Step 2: Calculate the total initial weight
The total weight of A and B can be calculated as:
- Total weight = Weight of A + Weight of B = 7x + 8x = 15x

### Step 3: Calculate the new weight of A after the increase
A's weight increases by 10%. Therefore, the new weight of A is:
- New weight of A = 7x + (10% of 7x) = 7x + 0.1 * 7x = 7x * (1 + 0.1) = 7x * 1.1 = 7.7x

### Step 4: Calculate the total weight after the increase
The total weight of A and B increases by 20%. Therefore, the new total weight is:
- New total weight = 15x + (20% of 15x) = 15x + 0.2 * 15x = 15x * (1 + 0.2) = 15x * 1.2 = 18x

### Step 5: Set up the equation for B's new weight
Let the new weight of B be represented as:
- New weight of B = Total new weight - New weight of A = 18x - 7.7x = 10.3x

### Step 6: Calculate the increase in B's weight
The increase in B's weight can be calculated as:
- Increase in B's weight = New weight of B - Original weight of B = 10.3x - 8x = 2.3x

### Step 7: Calculate the percentage increase in B's weight
The percentage increase in B's weight is given by:
- Percentage increase = (Increase in B's weight / Original weight of B) * 100
- Percentage increase = (2.3x / 8x) * 100 = (2.3 / 8) * 100 = 28.75%

### Final Answer
The percentage increase in B's weight is **28.75%**.

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