Question

If the SP of 10 pens is equal to the CP of 11 pens, find the profit percent.

Answer 1

Hint: Assume the cost price of 1 pen be Rs. x. Now, get the cost price of 10 pens and the cost price of 11 pens. It is given that the selling price of 10 pens is equal to the cost price of 11 pens. Now, calculate the profit by using the formula, Profit = Selling price of 10 pens – Cost price of 10 pens. Then, calculate the profit percentage by using the formula, \[\text{Profit Percentage of 10 pens=}\dfrac{\text{Profit made by selling 10 pens}}{\text{Cost}\,\text{price of 10 pens}}\text{ }\!\!\times\!\!\text{ 100}\] . Now, solve it further.

Complete step-by-step solution -
Let us assume the cost price of one pen is Rs. x.
The cost price of 10 pens = Rs. 10x ……………………………(1)
The cost price of 11 pens = Rs. 11x ………………………….(2)
According to the question, it is given that the selling price of 10 pens is equal to the cost price of 11 pens.
From equation (2), we have the cost price of 11 pens which is equal to Rs. 11x.
So, the selling price of 10 pens = Rs. 11x ………………………….(3)
We know the formula, Profit = Selling price of 10 pens – Cost price of 10 pens ………………….(4)
Putting the values from equation (1) and equation (3) in equation (4), we get
Profit = Rs. 11x – Rs. 10x = Rs. x ……………………(5)
We have to find the percentage of the profit after selling the pens.
We know the formula to find the percentage of profit,
\[\text{Profit Percentage of 10 pens=}\dfrac{\text{Profit made by selling 10 pens}}{\text{Cost}\,\text{price of 10 pens}}\text{ }\!\!\times\!\!\text{ 100}\] ……………………….(6)
From equation (5), we have the value of profit and from equation (1), we have the cost price of 10 pens.
Now, putting these values in equation (6), we get
\[\text{Profit Percentage of 10 pens=}\dfrac{Rs.x}{Rs.10x}\text{ }\!\!\times\!\!\text{ 100=}\dfrac{100}{10}=10\] .
Hence, the profit percentage is equal to 10%.

Note: In this question, one might make a mistake and take the cost price of 11 pens as the cost price while finding the percentage of profit by selling 10 pens. We cannot take the cost price of 11 pens as the cost price while finding the percentage of profit by selling 10 pens because we are selling 10 pens, so we have to take the cost price of 10 pens only.