A shopkeeper sells two watches for Rs. 300 each. On one he gains 20% and on the other, he loses 20%. His gain or loss percent in the whole transaction is :

To solve this problem, we need to understand that when two items are sold at the same price, one at a gain of x% and the other at a loss of x%, the seller always incurs a loss, irrespective of the value of x. This is a standard result in profit and loss problems.

Here's the step-by-step solution:

1. The shopkeeper sells two watches for Rs. 300 each. So, the total selling price (S.P.) of the two watches is Rs. 600.

2. On one watch, he gains 20%. This means the cost price (C.P.) of this watch is 100/120 * 300 = Rs. 250.

3. On the other watch, he loses 20%. This means the cost price (C.P.) of this watch is 100/80 * 300 = Rs. 375.

4. So, the total cost price (C.P.) of the two watches is Rs. 250 + Rs. 375 = Rs. 625.

5. The total selling price (S.P.) of the two watches is Rs. 600.

6. Therefore, the shopkeeper incurs a loss in the transaction because the total cost price is more than the total selling price.

7. The loss % is calculated as (Loss / C.P.) * 100. Here, Loss = C.P. - S.P. = Rs. 625 - Rs. 600 = Rs. 25.

8. So, the loss % = (25 / 625) * 100 = 4%.

Therefore, the shopkeeper incurs a loss of 4% in the whole transaction.