A person bought two bicycles for 1600 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the second at 10% profit, he would get 5 more. The difference of the cost price of the two bicycles was

Let C.P. of first bicycle = $$100x$$

=> C.P. of second bicycle = 1600 - $$100x$$

case 1 : First at 10% profit and second at 20%

=> Profit on first bicycle = $$\frac{10}{100} * 100x = 10x$$

and Profit on second bicycle = $$\frac{20}{100} * (1600-100x) = 320 - 20x$$

=> Total profit in case 1 = $$10x+320-20x = 320 - 10x$$

case 2 : First at 20% profit and second at 10%

=> Profit on first bicycle = $$\frac{20}{100} * 100x = 20x$$

and Profit on second bicycle = $$\frac{10}{100} * (1600-100x) = 160 - 10x$$

=> Total profit in case 2 = $$20x+160-10x = 160 + 10x$$

Now, according to the question :

=> $$320 - 10x + 5 = 160 + 10x$$

=> $$20x = 165 => x = 82.5$$

C.P. of bicycle 1 = 82.5*100 = 825

C.P. of bicycle 2 = 1600-825 = 775

=> Difference in cost prices = 825-775 = 50