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 in the cost price of the two bicycles was

Let the cost price of first bicycle be ₹ P.
Then, the cost price of second bicycle = ₹ (1600 - P)
According to the given condition,
[20% of P + 10% of (1600 - P )] - [10% of P + 20% of (1600 - P)] = 5
⇒ [(20P/100) + [10 x (1600 - P)]/100] - [(10P/100) + {20 x (1600 - P)}/100] = 5
⇒ (P/5 + (1600 - P)/10) - (P/10 + (1600 - P)/5) = 5
⇒ P/5 - P/10 + (1600 - P)/10 - (1600 - P)/5 = 5
⇒ 2P = 1600 + 50
∴ P = 1650/2 = 825
∴ Cost of second bicycle = (1600 - 825) = ₹ 775
∴ Required difference = 825 - 775 = ₹ 50