Two soaps `A` and `B` are given. Dimensions of `B` are `50%` more each than dimension of `A`. Soap content of `B` as compared to `A` is

Options

A. `1.5`
B. `2.25`
C. `3.375`
D. `4`

Answer

To solve the problem, we need to find the soap content of soap `B` as compared to soap `A`. The dimensions of soap `B` are 50% more than those of soap `A`.

### Step-by-Step Solution:

1. **Define the dimensions of soap A**:
Let the dimensions of soap `A` be:
- Length = \( l \)
- Breadth = \( b \)
- Height = \( h \)

2. **Calculate the dimensions of soap B**:
Since the dimensions of soap `B` are 50% more than those of soap `A`, we can express the dimensions of soap `B` as:
- Length of B = \( l + 0.5l = 1.5l \)
- Breadth of B = \( b + 0.5b = 1.5b \)
- Height of B = \( h + 0.5h = 1.5h \)

3. **Calculate the volume of soap A**:
The volume \( V_A \) of soap `A` is given by the formula:
\[ V_A = l \times b \times h \]

4. **Calculate the volume of soap B**:
The volume \( V_B \) of soap `B` can be calculated as:
\[ V_B = (1.5l) \times (1.5b) \times (1.5h) \]
Simplifying this:
\[ V_B = 1.5 \times 1.5 \times 1.5 \times l \times b \times h = 3.375 \times (l \times b \times h) = 3.375 \times V_A \]

5. **Determine the ratio of soap content of B to A**:
The soap content of `B` compared to `A` is given by the ratio of their volumes:
\[ \text{Soap content of B compared to A} = \frac{V_B}{V_A} = 3.375 \]

### Conclusion:
The soap content of `B` as compared to `A` is \( 3.375 \) times more.

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