A reduction of `20%` in the price of sugar enables a purchaser to obtain `8kg` more for `Rs.160`. Then the price per kg before reduction was

Options

A. Rs. `10`
B. Rs. `4`
C. Rs. `5`
D. Rs. `6`

Answer

To find the price per kg of sugar before the reduction, we can follow these steps:

### Step 1: Understand the problem
We know that a reduction of 20% in the price of sugar allows a purchaser to buy 8 kg more for Rs. 160. We need to find the price per kg before the reduction.

### Step 2: Set up the equations
Let the original price per kg of sugar be \( P \) rupees. After a 20% reduction, the new price per kg becomes:
\[ P_{\text{new}} = P - 0.2P = 0.8P \]

### Step 3: Calculate the quantity purchased before and after the price reduction
- The quantity of sugar that can be bought for Rs. 160 at the original price \( P \):
\[ \text{Quantity before} = \frac{160}{P} \]

- The quantity of sugar that can be bought for Rs. 160 at the new price \( 0.8P \):
\[ \text{Quantity after} = \frac{160}{0.8P} = \frac{160}{\frac{4}{5}P} = \frac{160 \times 5}{4P} = \frac{200}{P} \]

### Step 4: Set up the equation based on the increase in quantity
According to the problem, the increase in quantity is 8 kg:
\[ \text{Quantity after} - \text{Quantity before} = 8 \]
Substituting the quantities:
\[ \frac{200}{P} - \frac{160}{P} = 8 \]

### Step 5: Simplify the equation
Combine the fractions:
\[ \frac{200 - 160}{P} = 8 \]
This simplifies to:
\[ \frac{40}{P} = 8 \]

### Step 6: Solve for \( P \)
To find \( P \), multiply both sides by \( P \) and then by 8:
\[ 40 = 8P \]
Now, divide both sides by 8:
\[ P = \frac{40}{8} = 5 \]

### Conclusion
The price per kg of sugar before the reduction was Rs. 5.

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