A man bought a bike and a car for ₹500000. He sold the bike at a gain of 20% and the car at a loss of 10%, thereby gaining 5% on whole. The cost (in ₹) of the bike is:

Let's assume the cost price of a bike and a car is B and C respectively.

A man bought a bike and a car for ₹500000.

B + C = 500000    Eq.(i)

He sold the bike at a gain of 20% and the car at a loss of 10%, thereby gaining 5% on whole.

(100+20)% of B + (100-10)% of C = 500000 of (100+5)%

120% of B + 90% of C = 500000 of 105%

$$120B + 90C = 500000\times105$$
$$4B + 3C = 50000\times35$$

4B + 3C = 1750000    Eq.(ii)

Mulitply Eq.(i) by 3.

3B + 3C = 1500000    Eq.(iii)

Eq.(ii)-Eq.(iii)

4B + 3C - (3B + 3C) = 1750000-1500000

4B + 3C - 3B - 3C = 250000

Cost price of the bike = B = ₹250000