Due to reduction of `25%` in price of oranges a customer can purchase 4 oranges more for ₹ 16. What is original price of an orange?

Options

A. Rs 1
B. ₹ 1.33
C. ₹ 1.5
D. ₹ 1.6

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Define the original price
Let the original price of an orange be \( P \). According to the problem, there is a reduction of 25% in the price.

**Hint:** Remember that a 25% reduction means you are paying 75% of the original price.

### Step 2: Calculate the new price
The new price after a 25% reduction can be calculated as:
\[ \text{New Price} = P - 0.25P = 0.75P \]

**Hint:** You can express the reduction as a fraction of the original price.

### Step 3: Set up the equation for the number of oranges
The customer can buy 4 more oranges for ₹16 after the price reduction. Let’s denote the number of oranges that can be bought at the original price as \( N \). Therefore, the number of oranges that can be bought at the new price is \( N + 4 \).

Using the price, we can express the number of oranges:
- At the original price:
\[ N = \frac{16}{P} \]
- At the new price:
\[ N + 4 = \frac{16}{0.75P} \]

**Hint:** Use the formula for the number of items that can be purchased with a given amount of money.

### Step 4: Substitute and simplify the equation
Now, substituting \( N \) in the second equation:
\[ \frac{16}{P} + 4 = \frac{16}{0.75P} \]

To eliminate the fractions, multiply through by \( 0.75P \):
\[ 0.75P \left(\frac{16}{P} + 4\right) = 16 \]
This simplifies to:
\[ 12 + 3P = 16 \]

**Hint:** When multiplying through by a common denominator, make sure to distribute correctly.

### Step 5: Solve for \( P \)
Now, rearranging the equation:
\[ 3P = 16 - 12 \]
\[ 3P = 4 \]
\[ P = \frac{4}{3} \]

**Hint:** Isolate the variable by performing inverse operations.

### Step 6: Calculate the original price
Thus, the original price of an orange is:
\[ P = \frac{4}{3} \text{ or } 1.33 \text{ (approximately)} \]

**Hint:** Convert the fraction to a decimal if needed for clarity.

### Final Answer
The original price of an orange is ₹1.33 (or ₹4/3).

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