Mohit went to a shop to buy 50 kg of rice . He buys two varieties of rice which cost him Rs `4.50` per kg and rs `5.00` per kg. He spends a total of Rs 240. What was the quantity of less expensive rice bought by him ?

Options

A. 20 kg
B. 25 kg
C. 30 kg
D. 35 kg

Answer

To solve the problem, we need to find out how much of the less expensive rice Mohit bought. We can set up a system of equations based on the information provided.

### Step-by-Step Solution:

1. **Define Variables**:
Let \( X \) be the quantity of rice that costs Rs 4.50 per kg (less expensive rice).
Let \( Y \) be the quantity of rice that costs Rs 5.00 per kg (more expensive rice).

2. **Set Up the Equations**:
From the problem, we know two things:
- The total weight of rice is 50 kg:
\[ X + Y = 50 \quad \text{(Equation 1)} \]
- The total cost of the rice is Rs 240:
\[ 4.5X + 5Y = 240 \quad \text{(Equation 2)} \]

3. **Solve Equation 1 for Y**:
Rearranging Equation 1 gives:
\[ Y = 50 - X \quad \text{(Equation 3)} \]

4. **Substitute Equation 3 into Equation 2**:
Now, substitute \( Y \) from Equation 3 into Equation 2:
\[ 4.5X + 5(50 - X) = 240 \]

5. **Simplify the Equation**:
Expanding the equation:
\[ 4.5X + 250 - 5X = 240 \]
Combine like terms:
\[ -0.5X + 250 = 240 \]

6. **Isolate X**:
Subtract 250 from both sides:
\[ -0.5X = 240 - 250 \]
\[ -0.5X = -10 \]
Now, divide both sides by -0.5:
\[ X = \frac{-10}{-0.5} = 20 \]

7. **Find Y**:
Substitute \( X \) back into Equation 3 to find \( Y \):
\[ Y = 50 - 20 = 30 \]

8. **Conclusion**:
The quantity of less expensive rice (Rs 4.50 per kg) that Mohit bought is \( \boxed{20} \) kg.