A person buys two watches for a total sum of Rs. 1,000. He sells one watch at a loss of 5% and the other at a gain of 20% and on the whole, he gains Rs. 50. Th e cost prices of the two watches are:

Let us assume the cost of 2 watches to be 100a and 100b.
100a + 100b = 1000 ==> a + b = 10.
Selling price of 1st watch after 5% loss = 0.95*100a = 95a.
Selling price of 2nd watch after 20% gain = 1.20*100b = 120b.
Total selling price => 95a + 120b = 1050.
We will multiple the 1st equation with 95 and subtract it from the 2nd:
25b = 100 ==> b = 4 and a = 6.
The Costs of the 2 watches come out to be 600 and 400 i.e. Option C.