**Example 1**. A shopkeeper bought two TV sets at Rs. 10,000 each. He sold one at a profit 10% and the other at a loss of 10%. Find whether he made an overall profit or loss.

**Example 2**. A shopkeeper sold two TV sets at Rs. 10,000 each. He sold one at a profit 10% and the other at a loss of 10%. Find whether he made an overall profit or loss.

Of course, you can find the solution just below, but it is highly recommended that, you first try to solve it on your own.

Just remember the words of Paul Halmos, who says “**the only way to learn mathematics is to do mathematics**”.

The questions given above are not same! First, make sure of it.

The first question is different from the second only with respect to the terms **bought** and **sold**. The rest all are same. Due to these terms, how the behaviour of a question of profit and loss will change, that is the main point of discussion here. Let’s see the solution.

**Solution 1**. In this question, the C.P of each of the two TV sets is given (so that we know the total C.P) and we need to find the total S.P.

Cost Price (C.P) of the first and second TV sets are Rs.10,000 each. Therefore, total cost price = Rs. (10,000 + 10,000) = Rs.20,000. To find the total profit/ loss in this transaction, we need to find the total Selling Price (S.P). We know the following formulas for finding S.P:

In the first case, C.P = Rs.10,000 and profit = 10%. Hence

In the second case, C.P = Rs.10,000 and loss = 10%. Hence

Therefore, total S.P = Rs. (11,000 + 9,000) = Rs. 20,000.

Since total C.P = total S.P, there is no profit or loss in this transaction.

**Alternatively**, we can find the total profit in the first transaction and the total loss in the second transaction. Then we will compare the total profit and loss.

Profit occurred in the first transaction

Loss occurred in the second transaction

Since the amount of profit and loss are same, there is no profit or loss in this transaction.

As another alternative, we can use the **unitary method** to solve the given question. Just agree to the facts: in case of profit, if C.P is Rs.100 then S.P is Rs.110 and in case of loss, if C.P is Rs.100 then S.P is Rs.90. We need to find the respective S.P using this.

*In the first case*,

If C.P is Rs.100 then S.P is Rs.110

If C.P is Rs.1 then S.P is Rs.(110/100) = Rs.(11/10)

If C.P is Rs.10,000 then S.P is Rs.(11/10) × 10,000 = Rs.11,000.

*In the second case*,

If C.P is Rs.100 then S.P is Rs.90

If C.P is Rs. 1 then S.P is Rs. (90/100) = Rs. (9/10)

If C.P is Rs. 10,000 then S.P is Rs. (9/10) × 10,000 = Rs. 9,000.

As before, total C.P is Rs. 10,000 + Rs. 10,000 = Rs. 20,000 and total S.P is Rs. (11,000 + 9,000) = Rs. 20,000.

Since total C.P = total S.P, there is no profit or loss in this transaction.

**Solution 2**. The second example is totally different from the first one. In this question, the S.P of each of the two TV sets is given (so that we know the total S.P) and we need to find the total C.P.

Selling Price (S.P) of the first and second TV sets are ₹10,000 each. Therefore, total selling price = Rs. (10,000 + 10,000) = Rs. 20,000. To find the total profit/ loss in this transaction, we need to find the total Cost Price (C.P). We know the following formulas for finding C.P:

In the first case, S.P = Rs. 10,000 and profit = 10%. Hence

In the second case, S.P = Rs. 10,000 and loss = 10%. Hence

Since total C.P > total S.P, there is a loss in this transaction.

As another alternative, we can use the **unitary method** to solve the given question. Here, we need to find the respective C.P using this.

*In the first case*,

If S.P is Rs. 110 then C.P is Rs. 100

If S.P is Rs. 1 then C.P is Rs. (100/110) = Rs. (10/11)

*In the second case*,

If S.P is Rs. 90 then C.P is Rs. 100

If S.P is Rs. 1 then C.P is Rs. (100/90) = Rs. (10/9)

Since total C.P > total S.P, there is a loss in this transaction.