Question

If the cost price of 11 shirts is equal to the selling price of 10 shirts, find the percentage profit or loss.

Answer 1

Hint: First of all, take the C.P of 1 shirt as x. From this, find the C.P of 10 shirts and 11 shirts. Now, equate the C.P of 11 shirts to S.P of 10 shirts. Now, use Profit = S.P – C.P and Profit % \[=\dfrac{\text{Profit}}{\text{C}\text{.P}}\times 100\] to get the desired result.

Complete step-by-step answer:

We are given that the cost price of 11 shirts is equal to the selling price of 10 shirts. We have to find the percentage of profit or loss. Before proceeding with this question, let us see a few terms.
Cost Price (C.P): This is the amount paid by the shopkeeper to purchase a product.
Selling Price (S.P): This is the amount at which a product sold by the shopkeeper.
Profit (P): This is the amount gained after selling a product more than its cost price.
Profit = S.P – C.P
Profit % \[=\dfrac{\text{Profit}}{\text{C}\text{.P}}\times 100\]
Loss (L): This is the amount the seller gets after selling the product less than its cost price.
Loss = C.P – S.P
Loss % \[=\dfrac{\text{Loss}}{\text{C}\text{.P}}\times 100\]
Now, let us consider our question. Let us take the cost price (C.P) of one shirt to be x. Now, the C.P of 11 shirts would be 11x. Also, the C.P of 10 shirts would be 10x. We are given that C.P of 11 shirts is equal to the selling price (S.P) of 10 shirts. So, we get,
S.P of 10 shirts = C.P of 11 shirts
So, we get, S.P of 10 shirts = 11x
Here, we can see that S.P of 10 shirts = 11x and C.P of 10 shirts = 10x
We know that here S.P is greater than C.P. So, there will be profit.
Now, we know that Profit = S.P – C.P
By substituting S.P = 11x and C.P = 10x, we get,
Profit = 11x – 10x = x
We also know that Profit % \[=\dfrac{\text{Profit}}{\text{C}\text{.P}}\times 100\]
By substituting the value of Profit = x and C.P = 10x, we get,
Profit % \[=\dfrac{x}{10x}\times 100\]
\[=\dfrac{100}{10}\]
= 10 %
So, we have got a profit of 10 %.

Note: In these types of questions, students must remember to use the corresponding values of C.P and S.P in a formula. For example, if we substitute the C.P of 10 shirts in a formula, S.P should also be of 10 shirts only and not of any other value. Also, it would be very beneficial for the students if they remember the formulas of profit and loss percent which are very useful while solving the questions related to this chapter.