A speculator lost 35% of his capital in 1 operation, and lost 40% of the remainder in 2nd operation.

Question

Here is the complete problem:

A speculator lost 35% of his capital in one operation, and lost 40% of the remainder in a 2nd operation. If he then had 15,600, how much had he at first?

Answer 1

Let C be the original capital. After losing in the first operation what remained was 0.65C.

After losing 40% of this in the second operation he is left with 60% of this remainder=0.60×0.65C=0.39C=15600.

So C=15600/0.39=40,000.

CHECK

1st operation: he lost 35% of 40,000=14,000, leaving 26,000.

2nd operation: he lost 40% of 26000=10,400, leaving 15,600.