A reduction of 20% in the price of mangoes enables a person to purchase 12 more for Rs 15. Find the price of 16 mangoes before reduction?

Answer

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

### Step 1: Understand the Price Reduction
Let the original price of one mango be \( P \) (in Rs). A reduction of 20% means the new price becomes:
\[ \text{New Price} = P - 0.2P = 0.8P \]

### Step 2: Determine the Number of Mangoes Purchased
According to the problem, after the price reduction, a person can buy 12 more mangoes for Rs 15. Let's denote the number of mangoes that could be bought before the price reduction as \( N \).

The number of mangoes that can be bought after the price reduction is:
\[ N + 12 \]

### Step 3: Set Up the Equation
The total cost for buying mangoes before the reduction is:
\[ N \times P = 15 \]
Thus, the number of mangoes before the reduction is:
\[ N = \frac{15}{P} \]

After the price reduction, the total cost for buying mangoes is:
\[ (N + 12) \times 0.8P = 15 \]

### Step 4: Substitute \( N \) in the New Equation
Substituting \( N \) from the first equation into the second equation:
\[ \left(\frac{15}{P} + 12\right) \times 0.8P = 15 \]

### Step 5: Simplify the Equation
Expanding the equation gives:
\[ 0.8P \times \frac{15}{P} + 0.8P \times 12 = 15 \]
This simplifies to:
\[ 12 + 9.6P = 15 \]

### Step 6: Solve for \( P \)
Rearranging the equation:
\[ 9.6P = 15 - 12 \]
\[ 9.6P = 3 \]
\[ P = \frac{3}{9.6} = \frac{5}{16} \text{ Rs} \]

### Step 7: Find the Price of 16 Mangoes Before Reduction
Now, we need to find the price of 16 mangoes before the reduction:
\[ \text{Price of 16 mangoes} = 16 \times P = 16 \times \frac{5}{16} = 5 \text{ Rs} \]

### Final Answer
The price of 16 mangoes before the reduction is Rs 5.

---