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 use the concept of joint variation. The weight \( W \) of the sumo wrestler varies jointly with his height \( h \) and age \( a \). This relationship can be expressed mathematically as:

\[ W = k \cdot h \cdot a \]

where \( k \) is the constant of variation.

### Step 1: Find the constant of variation \( k \)

We are given that when the height \( h = 1.2 \) m and the age \( a = 20 \) years, the weight \( W = 48 \) kg. We can substitute these values into the equation to find \( k \):

\[ 48 = k \cdot 1.2 \cdot 20 \]

Now, calculate \( 1.2 \cdot 20 \):

\[ 1.2 \cdot 20 = 24 \]

So, we can rewrite the equation as:

\[ 48 = k \cdot 24 \]

To find \( k \), divide both sides by 24:

\[ k = \frac{48}{24} = 2 \]

### Step 2: Use the constant \( k \) to find the weight for the new height and age

Now we need to find the weight when the height \( h = 1.5 \) m and the age \( a = 30 \) years. We can substitute these values along with the constant \( k \) into the original equation:

\[ W = 2 \cdot 1.5 \cdot 30 \]

Now, calculate \( 1.5 \cdot 30 \):

\[ 1.5 \cdot 30 = 45 \]

So, we can rewrite the equation as:

\[ W = 2 \cdot 45 \]

Now, calculate \( 2 \cdot 45 \):

\[ W = 90 \]

### Conclusion

The weight of the sumo wrestler when his height is 1.5 meters and age is 30 years is **90 kg**.

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