A reduction of 20% in the price of an apple enables a man to buy 10 apples more for Rs. 54. The reduced price of apples per dozen is

Options

A. Rs.4.32
B. Rs.12.96
C. Rs.10.80
D. Rs.14.60

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript and break it down into clear steps.

### Step 1: Define the original price of an apple
Let the original price of an apple be Rs. X.

### Step 2: Calculate the reduced price of an apple
Since there is a reduction of 20%, the new price of an apple becomes:
\[ \text{Reduced Price} = X - 0.20X = 0.80X = \frac{4X}{5} \]

### Step 3: Determine the number of apples bought at the original price
At the original price, the number of apples that can be bought for Rs. 54 is:
\[ \text{Number of apples at original price} = \frac{54}{X} \]

### Step 4: Determine the number of apples bought at the reduced price
At the reduced price, the number of apples that can be bought for Rs. 54 is:
\[ \text{Number of apples at reduced price} = \frac{54}{\frac{4X}{5}} = \frac{54 \times 5}{4X} = \frac{270}{4X} = \frac{135}{2X} \]

### Step 5: Set up the equation based on the increase in the number of apples
According to the problem, the man can buy 10 more apples at the reduced price. Therefore, we can set up the equation:
\[ \frac{135}{2X} - \frac{54}{X} = 10 \]

### Step 6: Simplify the equation
To simplify, we need a common denominator. The common denominator for \(2X\) and \(X\) is \(2X\):
\[ \frac{135 - 108}{2X} = 10 \]
\[ \frac{27}{2X} = 10 \]

### Step 7: Solve for X
Cross-multiplying gives:
\[ 27 = 20X \implies X = \frac{27}{20} = 1.35 \]

### Step 8: Calculate the reduced price per dozen
Now, we need to find the reduced price of apples per dozen. The reduced price per apple is:
\[ \text{Reduced Price} = \frac{4X}{5} = \frac{4 \times 1.35}{5} = \frac{5.4}{5} = 1.08 \]
Thus, the reduced price per dozen (12 apples) is:
\[ \text{Reduced Price per dozen} = 12 \times 1.08 = 12.96 \]

### Final Answer
The reduced price of apples per dozen is Rs. 12.96.

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