Due to a reduction of `10%` in the price of milk a person is able to buy 6.2 lt more for Rs. 1116. Find the reduced price of milk per litre ?

Options

A. 20
B. 16
C. 15
D. 18

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Problem
We know that due to a reduction of 10% in the price of milk, a person can buy 6.2 liters more for Rs. 1116. We need to find the reduced price of milk per liter.

### Step 2: Let’s Define Variables
Let the original price of milk per liter be \( P \) (in Rs).

### Step 3: Calculate the Reduced Price
Since the price is reduced by 10%, the reduced price \( P' \) can be calculated as:
\[ P' = P - 0.10P = 0.90P \]

### Step 4: Calculate the Quantity of Milk Bought
Using the original price \( P \), the quantity of milk that could be bought for Rs. 1116 is:
\[ \text{Quantity at original price} = \frac{1116}{P} \]

Using the reduced price \( P' \), the quantity of milk that can be bought is:
\[ \text{Quantity at reduced price} = \frac{1116}{P'} \]
Substituting \( P' \):
\[ \text{Quantity at reduced price} = \frac{1116}{0.90P} \]

### Step 5: Set Up the Equation
According to the problem, the difference in quantity bought due to the price reduction is 6.2 liters:
\[ \frac{1116}{0.90P} - \frac{1116}{P} = 6.2 \]

### Step 6: Simplify the Equation
To simplify, we can factor out \( 1116 \):
\[ 1116 \left( \frac{1}{0.90P} - \frac{1}{P} \right) = 6.2 \]
Finding a common denominator:
\[ \frac{1116(P - 0.90P)}{0.90P^2} = 6.2 \]
This simplifies to:
\[ \frac{1116(0.10P)}{0.90P^2} = 6.2 \]
\[ \frac{111.6}{0.90P} = 6.2 \]

### Step 7: Solve for P
Cross-multiplying gives:
\[ 111.6 = 6.2 \times 0.90P \]
Calculating \( 6.2 \times 0.90 \):
\[ 111.6 = 5.58P \]
Now, solving for \( P \):
\[ P = \frac{111.6}{5.58} \approx 20 \]

### Step 8: Calculate the Reduced Price
Now, we can find the reduced price \( P' \):
\[ P' = 0.90P = 0.90 \times 20 = 18 \]

### Final Answer
The reduced price of milk per liter is Rs. 18.

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