A reduction of 10% in the price of sugar enables a housewife to buy 6.2 kg more for 1116. The reduced price per kg is

Options

A. 12
B. 14
C. 16
D. 18

Answer

To solve the problem step by step, we need to determine the reduced price per kg of sugar after a 10% reduction that allows the housewife to buy 6.2 kg more sugar for Rs 1116.

### Step 1: Define the original price of sugar.
Let the original price of sugar be \( P \) per kg.

### Step 2: Calculate the reduced price of sugar.
Since there is a reduction of 10%, the reduced price \( P' \) can be calculated as:
\[ P' = P - 0.1P = 0.9P \]

### Step 3: Determine the amount of sugar bought at the original price.
The amount of sugar that can be bought at the original price for Rs 1116 is:
\[ \text{Quantity at original price} = \frac{1116}{P} \]

### Step 4: Determine the amount of sugar bought at the reduced price.
The amount of sugar that can be bought at the reduced price for Rs 1116 is:
\[ \text{Quantity at reduced price} = \frac{1116}{P'} \]
Substituting \( P' \):
\[ \text{Quantity at reduced price} = \frac{1116}{0.9P} = \frac{1116}{0.9P} \]

### Step 5: Set up the equation based on the increase in quantity.
According to the problem, the difference in quantity bought at the reduced price and the original price is 6.2 kg:
\[ \frac{1116}{0.9P} - \frac{1116}{P} = 6.2 \]

### Step 6: Simplify the equation.
To simplify the left side, we can find a common denominator:
\[ \frac{1116P - 1116 \times 0.9P}{0.9P^2} = 6.2 \]
This simplifies to:
\[ \frac{1116 \times 0.1P}{0.9P^2} = 6.2 \]
Now, multiply both sides by \( 0.9P^2 \):
\[ 111.6P = 6.2 \times 0.9P^2 \]

### Step 7: Rearranging the equation.
Rearranging gives:
\[ 6.2 \times 0.9P^2 - 111.6P = 0 \]
This can be written as:
\[ 5.58P^2 - 111.6P = 0 \]

### Step 8: Factor out \( P \).
Factoring out \( P \):
\[ P(5.58P - 111.6) = 0 \]
Since \( P \) cannot be zero, we can set the other factor to zero:
\[ 5.58P - 111.6 = 0 \]

### Step 9: Solve for \( P \).
Solving for \( P \):
\[ 5.58P = 111.6 \implies P = \frac{111.6}{5.58} \approx 20 \]

### Step 10: Calculate the reduced price.
Now, we can find the reduced price \( P' \):
\[ P' = 0.9 \times 20 = 18 \]

Thus, the reduced price per kg of sugar is **Rs 18**.