A person bought 60 quintals of rice of two different sorts for Rs.4642.50.The better sort costs Rs.80 per quintal and the worse Rs. 75.50 per quintal. How many quintals were there of each sort ?

Options

A. 25 quintals, 35 quintals
B. 20 quintals, 40 quintals
C. 32 quintals, 28 quintals
D. None of these

Answer

To solve the problem of how many quintals of each sort of rice were bought, we can follow these steps:

### Step 1: Define the Variables
Let:
- \( x \) = quantity of better sort rice (in quintals)
- \( y \) = quantity of worse sort rice (in quintals)

### Step 2: Set Up the Equations
We know from the problem:
1. The total quantity of rice is 60 quintals:
\[ x + y = 60 \]
2. The total cost of the rice is Rs. 4642.50, where the better sort costs Rs. 80 per quintal and the worse sort costs Rs. 75.50 per quintal:
\[ 80x + 75.50y = 4642.50 \]

### Step 3: Solve the First Equation for One Variable
From the first equation, we can express \( y \) in terms of \( x \):
\[ y = 60 - x \]

### Step 4: Substitute into the Second Equation
Now substitute \( y \) in the second equation:
\[ 80x + 75.50(60 - x) = 4642.50 \]

### Step 5: Expand and Simplify
Expanding the equation gives:
\[ 80x + 4530 - 75.50x = 4642.50 \]
Combine like terms:
\[ (80 - 75.50)x + 4530 = 4642.50 \]
\[ 4.50x + 4530 = 4642.50 \]

### Step 6: Isolate \( x \)
Subtract 4530 from both sides:
\[ 4.50x = 4642.50 - 4530 \]
\[ 4.50x = 112.50 \]
Now divide by 4.50:
\[ x = \frac{112.50}{4.50} = 25 \]

### Step 7: Find \( y \)
Now substitute \( x \) back into the equation for \( y \):
\[ y = 60 - x = 60 - 25 = 35 \]

### Step 8: Conclusion
The quantities of rice are:
- Quantity of better sort rice: **25 quintals**
- Quantity of worse sort rice: **35 quintals**

### Summary of the Solution
- Better sort rice: 25 quintals
- Worse sort rice: 35 quintals

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