An Increase of 20% in the price of mangoes enables a person to purchase 4 mangoes less for 40. The price of 15 mangoes be fore Increase was

Options

A. 10
B. 15
C. 20
D. 25

Answer

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

### Step 1: Understand the Problem
We are given that an increase of 20% in the price of mangoes allows a person to buy 4 mangoes less for 40. We need to find the price of 15 mangoes before the increase.

### Step 2: Define Variables
Let the original price of 1 mango be \( P \). After a 20% increase, the new price becomes:
\[ P' = P + 0.2P = 1.2P \]

### Step 3: Set Up the Equation for Quantity
Let the original quantity of mangoes that can be purchased for 40 be \( Q \). Thus, we have:
\[ Q = \frac{40}{P} \]
After the price increase, the new quantity of mangoes that can be purchased for the same amount (40) is:
\[ Q' = \frac{40}{1.2P} \]

### Step 4: Relate the Quantities
According to the problem, the new quantity is 4 less than the original quantity:
\[ Q' = Q - 4 \]
Substituting the expressions for \( Q \) and \( Q' \):
\[ \frac{40}{1.2P} = \frac{40}{P} - 4 \]

### Step 5: Solve the Equation
To eliminate the fractions, multiply through by \( 1.2P \):
\[ 40 = 1.2 \cdot 40 - 4 \cdot 1.2P \]
This simplifies to:
\[ 40 = 48 - 4.8P \]
Rearranging gives:
\[ 4.8P = 48 - 40 \]
\[ 4.8P = 8 \]
Now, solving for \( P \):
\[ P = \frac{8}{4.8} = \frac{80}{48} = \frac{5}{3} \]

### Step 6: Find the Price of 15 Mangoes
Now that we have the price of one mango, we can find the price of 15 mangoes:
\[ \text{Price of 15 mangoes} = 15 \times P = 15 \times \frac{5}{3} = 25 \]

### Final Answer
The price of 15 mangoes before the increase was **25**.

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