Weight of a sumo is jointly varies as his height and his age. When height is 1.2 m and age is 20 years his weight is 48 kg. Find the weight of the sumo when his height is 1.5 metre and age is 30 years :

Options

A. 60 kg
B. 72 kg
C. 90 kg
D. 58 kg

Answer

To solve the problem, we need to find the weight of a sumo wrestler based on the given conditions using the concept of joint variation.

### Step-by-Step Solution:

1. **Understand the Joint Variation**:
The weight \( W \) of the sumo wrestler varies jointly with his height \( H \) and age \( A \). This can be expressed mathematically as:
\[ W = k \cdot H \cdot A \]
where \( k \) is the constant of variation.

2. **Substitute the Known Values**:
We know that when the height \( H = 1.2 \) m and age \( A = 20 \) years, the weight \( W = 48 \) kg. We can substitute these values into the equation to find \( k \):
\[ 48 = k \cdot 1.2 \cdot 20 \]

3. **Calculate the Constant \( k \)**:
First, calculate \( 1.2 \cdot 20 \):
\[ 1.2 \cdot 20 = 24 \]
Now, substitute this back into the equation:
\[ 48 = k \cdot 24 \]
To find \( k \), divide both sides by 24:
\[ k = \frac{48}{24} = 2 \]

4. **Use the Constant \( k \) to Find the New Weight**:
Now that we have \( k = 2 \), we can find the weight when the height \( H = 1.5 \) m and age \( A = 30 \) years:
\[ W = 2 \cdot 1.5 \cdot 30 \]

5. **Calculate \( 1.5 \cdot 30 \)**:
First, calculate \( 1.5 \cdot 30 \):
\[ 1.5 \cdot 30 = 45 \]
Now substitute this back into the equation for weight:
\[ W = 2 \cdot 45 = 90 \]

6. **Final Answer**:
Therefore, the weight of the sumo wrestler when his height is 1.5 m and age is 30 years is:
\[ W = 90 \text{ kg} \]