Question

A grocer bought 15 sweets at Rs 72. He sold them at a gain of Rs 18. Find his profit percentage. Also, find the selling price of 20 sweets.

Answer 1

Hint: This question is based on unitary method as well as profit and loss. To find the profit percentage, we need to find the selling price of 15 sweets. This is done by adding the gain to the cost price. Then, we will find the profit percentage by the relation pp = $\dfrac{\text{sp}-\text{cp}}{\text{cp}}\times 100$, where pp is the percentage profit, sp is the selling price and cp is the cost price of the sweets. To find the selling price of 20 sweets, we will make use of a unitary method. First, we will find the selling price of each sweet by dividing the selling price of 15 sweets by 15. Then, we will multiply this amount with 20 and the result will be the selling price of 20 sweets.

Complete step by step answer:
It is given that the cost price of 15 sweets is Rs 72 and he sold them all at a gain of Rs 18.
Therefore, the selling price for 15 sweets will be (72 + 18) = Rs 90.
Now, we will find the profit percentage by the relation pp = $\dfrac{\text{sp}-\text{cp}}{\text{cp}}\times 100$, where pp is the percentage profit, sp is the selling price and cp is the cost price of the sweets.
Therefore, pp = $\dfrac{90-72}{72}\times 100=\dfrac{18}{72}\times 100$ = 0.25 × 100 = 25%
Hence, the profit percentage when the gain is Rs 18 is 25%.
We have calculated that the selling price of 15 sweets is Rs 90. Thus, we will find the selling price of 1 sweet by dividing the selling price of 15 sweets by 15.
Therefore, selling price of 1 sweet = $\dfrac{90}{15}$ = Rs 6.
To find the selling price of 20 sweets, we will multiply the selling price of 1 sweet by 20.
Therefore, selling price of 20 sweets = Rs $6\times20$ = Rs 120

Note: Students are advised to be well versed with the concepts of percentage as it will be very helpful for solving profit and loss questions. Profit percentage can directly be found by the relation profit percentage = $\dfrac{\text{gain}}{\text{cost}\ \text{price}}\times 100$.