Question

A reduction of 20% in the price of mangoes enables a man to buy 25 mangoes more for Rs.40. Find the reduced price of the basket that contains 200 mangoes.

• A. Rs. 100
• B. Rs. 75
• C. Rs. 60
• D. Rs. 64
• E. Rs. 80

Answer 1

The Correct Option is D

Step 1: Understand the problem.
A reduction of 20% in the price of mangoes enables a man to buy 25 more mangoes for Rs. 40. We need to find the reduced price of a basket that contains 200 mangoes.

Step 2: Let the original price of 1 mango be \( p \).
The original price of 1 mango is \( p \). For Rs. 40, the number of mangoes the man could buy at the original price is:
\( \text{Number of mangoes} = \frac{40}{p} \)

After a 20% reduction in the price of mangoes, the new price of 1 mango is \( 0.80p \). For Rs. 40, the number of mangoes the man can now buy is:
\( \text{New number of mangoes} = \frac{40}{0.80p} = \frac{40}{p} \times \frac{1}{0.80} = \frac{50}{p} \)

The increase in the number of mangoes is 25. Therefore, the equation is: \[ \frac{50}{p} - \frac{40}{p} = 25 \] Simplifying this: \[ \frac{10}{p} = 25 \] Solving for \( p \): \[ p = \frac{10}{25} = 0.4 \] So, the original price of 1 mango is Rs. 0.40.

Step 3: Calculate the reduced price of a basket of 200 mangoes.
The reduced price of 1 mango is \( 0.80 \times 0.40 = 0.32 \) rupees.
Therefore, the reduced price of a basket containing 200 mangoes is:
\( 200 \times 0.32 = 64 \) rupees.

Step 4: Conclusion.
The reduced price of the basket containing 200 mangoes is Rs. 64.

Final Answer:
The correct option is (D): Rs. 64.