Question

A fruits seller buys 100 kg of apples at the rate of Rs. 20 per kg. He sold \[\dfrac{2}{5}\]of the apples at a loss of \[7\% \]. At what rate must the remaining apples make a profit of \[15\% \]on the sale of all apples?
A. 19.06 %
B. 29.66 %
C. 79.56 %
D. 69.66 %

Answer 1

Hint: When a product is purchased in the view of selling it to the consumer in order to do business then, the price in which the product is bought by the seller is known as the cost price of the product and the price in which the seller sells the product to the consumer is known as selling of the product for the seller. If the selling price of the product is greater than the cost price of the product, then the difference in the prices can be termed as the profit or the gain on the product while at the same time if the selling price is less than the cost price of the product, then the difference in the price is known as the loss on the product. Profit per cent or, loss per cent of a product is always calculated on the cost price of the product.

Complete step-by-step solution:
Total apples is 100 and rate of apple per kg is Rs. 20 so,
Total Amount is \[100 \times 20 = 2000\]
The case I: He sold \[\dfrac{2}{5}\]of the total apples at a loss of \[7\% \]
\[\dfrac{2}{5}\]of the total apples is calculated as: \[100 \times \dfrac{2}{5} = 40\]
Cost of 1 kg apples = Rs 20
Cost of 40 kg apples = Rs 20 X 40= Rs800
And with 7% loss, the vendor got back = \[800 \times \left( {\dfrac{{100 - 7}}{{100}}} \right) = 744\]
So, a vendor sold 40kg apples at 744 with 7% loss.

Case II:
He must be selling the remaining apples to make a profit of \[15\% \]on the sale of all apples.
To find remaining apples, we have: \[1 - \dfrac{2}{5} = \dfrac{3}{5}\]
A remaining number of apples to be sold as of now: \[100 \times \dfrac{3}{5} = 60\]
Cost of 1 kg apples = Rs20
Cost of 100 kg apples = Rs 20 X 100= Rs2000
And a profit of 15% of the total cost
\[15\% \] Profit of all \[ = 2000 \times \left( {\dfrac{{100 + 15}}{{100}}} \right) = 2300\]
So to get an overall 15% profit, the vendor should sell the remaining 60 kg apples for:
Overall selling price= profit- loss \[ = 2300 - 744 = 1556\]
Price of remaining 60kg of apples= Rs. 1200
Required profit is \[(1556 - 1200) = 356\]
Hence, the profit percentage is calculated as:
\[
  P\% = \dfrac{{profit}}{{CP}} \times 100 \\
   = \dfrac{{356}}{{1200}} \times 100 \\
   = 29.66\% \\
 \]

Note: It is to be noted here that many a time, the marked price has been given in the question instead of selling price. So, be careful while reading the question as the marked price is the price which has been marked on the product by the seller but the selling price is the price of the product which the seller actually gets for the product after discount.