Question

A trader purchased 20 apples. Half of the stock was sold at a profit of 10% and with that money he purchased five mangoes. After that he sold his entire stock at a profit of 20% thereby gaining Rs.21. Find the cost of each mango.

• A. Rs.11
• B. Rs.10
• C. Rs.5
• D. Rs.9
• E. Rs. 7

Answer 1

The Correct Option is A

Step 1: Understand the problem.
A trader purchased 20 apples. He sold half of the apples (10 apples) at a profit of 10%. With the money earned, he bought 5 mangoes. After that, he sold all his remaining apples and mangoes at a profit of 20%, gaining a total of Rs. 21. We are asked to find the cost of each mango.

Step 2: Calculate the cost price of the apples.
Let the cost price of each apple be \( x \). Then, the total cost of 20 apples is \( 20x \).

Step 3: Calculate the revenue from selling 10 apples.
The first half of the apples (10 apples) were sold at a profit of 10%. The selling price of 10 apples will be:
Selling price of 10 apples = \( 10 \times x \times (1 + \frac{10}{100}) = 10 \times x \times 1.1 = 11x \)

Step 4: Purchase mangoes with the money earned.
The trader uses the Rs. \( 11x \) from selling the apples to buy 5 mangoes. So, the cost price of each mango is:
Cost of each mango = \( \frac{11x}{5} \)

Step 5: Calculate the total revenue from selling all apples and mangoes.
After selling the remaining 10 apples, he makes a profit of 20%. The selling price of the remaining 10 apples is:
Selling price of 10 apples = \( 10 \times x \times (1 + \frac{20}{100}) = 10 \times x \times 1.2 = 12x \)
The total revenue from selling all apples (20 apples) is:
Total revenue from apples = \( 11x + 12x = 23x \)
Now, the revenue from selling the 5 mangoes is:
Selling price of 5 mangoes = \( 5 \times \left(\frac{11x}{5} \times 1.2\right) = 11x \times 1.2 = 13.2x \)

So, the total revenue from all sales is:
Total revenue = \( 23x + 13.2x = 36.2x \)

Step 6: Calculate the total gain and solve for \( x \).
The trader's total gain is Rs. 21, so the total revenue minus the total cost price is Rs. 21:
Total revenue - Total cost price = 21
\( 36.2x - 20x = 21 \)
\( 16.2x = 21 \)
\( x = \frac{21}{16.2} = 1.296 \)

Step 7: Find the cost of each mango.
The cost of each mango is:
Cost of each mango = \( \frac{11x}{5} = \frac{11 \times 1.296}{5} = 11 \)

Step 8: Conclusion.
The cost of each mango is Rs. 11.

Final Answer:
The correct option is (A): Rs. 11.