A reduction of 20% in the price of oranges enables a man to buy 5 oranges more for Rs. 10/-. The price of an orange before reduction was:

Options

A. 20 paise
B. 40 paise
C. 50 paise
D. 60 paise

Answer

To solve the problem step-by-step, we need to find the original price of an orange before the reduction. Here’s how we can approach it:

### Step 1: Understand the problem
We know that a reduction of 20% in the price of oranges allows a man to buy 5 more oranges for Rs. 10. We need to find the original price of an orange before the reduction.

**Hint:** Identify the relationship between price, quantity, and expenditure.

### Step 2: Let the original price of one orange be \( P \).
The reduced price after a 20% reduction can be calculated as:
\[ \text{Reduced Price} = P - 0.2P = 0.8P \]

**Hint:** Remember that a 20% reduction means you are paying 80% of the original price.

### Step 3: Determine the number of oranges bought at the original price.
At the original price \( P \), for Rs. 10, the number of oranges that can be bought is:
\[ \text{Number of oranges at original price} = \frac{10}{P} \]

**Hint:** Use the formula for quantity which is expenditure divided by price.

### Step 4: Determine the number of oranges bought at the reduced price.
At the reduced price \( 0.8P \), for Rs. 10, the number of oranges that can be bought is:
\[ \text{Number of oranges at reduced price} = \frac{10}{0.8P} = \frac{10}{\frac{4}{5}P} = \frac{10 \times 5}{4P} = \frac{50}{4P} = \frac{25}{2P} \]

**Hint:** Simplifying fractions can help in understanding the relationship better.

### Step 5: Set up the equation based on the information given.
According to the problem, the difference in the number of oranges bought is 5:
\[ \frac{25}{2P} - \frac{10}{P} = 5 \]

**Hint:** This equation represents the increase in quantity due to the price reduction.

### Step 6: Solve the equation.
First, find a common denominator for the left side:
\[ \frac{25}{2P} - \frac{20}{2P} = 5 \]
This simplifies to:
\[ \frac{5}{2P} = 5 \]

Now, cross-multiply to solve for \( P \):
\[ 5 = 5 \times 2P \implies 5 = 10P \implies P = \frac{5}{10} = \frac{1}{2} \]

**Hint:** When solving equations, make sure to isolate the variable correctly.

### Step 7: Convert the price into rupees.
Since \( P = \frac{1}{2} \) rupees, the original price of one orange in rupees is:
\[ \text{Original Price} = 0.5 \text{ rupees} = 50 \text{ paise} \]

**Hint:** Remember to convert between different units if necessary.

### Final Answer:
The original price of an orange before the reduction was **50 paise** or **Rs. 0.50**.