Ramesh purchased 4kg rice & 5 kg wheat for Rs.180 and Suresh purchased 2kg rice & 15kg wheat for Rs.290. Then, find per kg price of wheat is what percent of per kg price of rice?

Options

A. A)`64% `
B. B)`90% `
C. C)`75% `
D. D)`82% `

Answer

To find the per kg price of wheat as a percentage of the per kg price of rice, we can follow these steps:

### Step-by-Step Solution:

1. **Set Up the Equations**:
- Let the price of rice be \( R \) (in Rs/kg) and the price of wheat be \( W \) (in Rs/kg).
- From Ramesh's purchase:
\[ 4R + 5W = 180 \quad \text{(Equation 1)} \]
- From Suresh's purchase:
\[ 2R + 15W = 290 \quad \text{(Equation 2)} \]

2. **Multiply Equation 2 by 2**:
- To eliminate \( R \), we can manipulate the equations. Multiply Equation 2 by 2:
\[ 4R + 30W = 580 \quad \text{(Equation 3)} \]

3. **Subtract Equation 1 from Equation 3**:
- Now, subtract Equation 1 from Equation 3:
\[ (4R + 30W) - (4R + 5W) = 580 - 180 \]
This simplifies to:
\[ 25W = 400 \]

4. **Solve for \( W \)**:
- Divide both sides by 25:
\[ W = \frac{400}{25} = 16 \quad \text{(Rs/kg)} \]
- So, the price of wheat is Rs 16 per kg.

5. **Substitute \( W \) back into Equation 1 to find \( R \)**:
- Substitute \( W = 16 \) into Equation 1:
\[ 4R + 5(16) = 180 \]
Simplifying gives:
\[ 4R + 80 = 180 \]
\[ 4R = 180 - 80 = 100 \]
\[ R = \frac{100}{4} = 25 \quad \text{(Rs/kg)} \]
- So, the price of rice is Rs 25 per kg.

6. **Calculate the Percentage**:
- Now, we need to find what percent the price of wheat is of the price of rice:
\[ \text{Percentage} = \left( \frac{W}{R} \right) \times 100 = \left( \frac{16}{25} \right) \times 100 \]
- Calculating this gives:
\[ \text{Percentage} = \frac{16 \times 100}{25} = 64\% \]

### Final Answer:
The per kg price of wheat is **64%** of the per kg price of rice.

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