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Mukesh purchased 1010 bicycles in 20172017, all at the same price. He sold six of these at a profit of 25%25 \% and the remaining four at a loss of 25%25 \%. If he made a total profit of Rs. 2000,2000, then his purchase price of a bicycle, in Rupees, was

Solution

✅ Correct Option: 1

Mukesh bought 10 bicycles at the same price each. He sold 6 at a 25% profit and 4 at a 25% loss, making a total profit of Rs. 2000. We need to find the purchase price of each bicycle.

When we sell something at a profit or loss, the actual profit/loss amount equals the percentage times the cost price.

Let the purchase price of each bicycle = xx rupees


Profit from each bicycle = 25% of xx = 0.25x0.25x

Total profit from 6 bicycles = 6×0.25x=1.5x6 \times 0.25x = 1.5x


Loss from each bicycle = 25% of xx = 0.25x0.25x

Total loss from 4 bicycles = 4×0.25x=x4 \times 0.25x = x


Net profit = Total profit - Total loss

Since Mukesh made a total profit of Rs. 2000:

2000=1.5x−x2000 = 1.5x - x

2000=0.5x2000 = 0.5x


0.5x=20000.5x = 2000

x=20000.5x = \frac{2000}{0.5}

x=4000x = 4000


Therefore, the purchase price of each bicycle was Rs. 4000.

In profit-loss problems, we always remember that the actual profit/loss amount equals the percentage times the original cost price. This makes setting up equations much easier!

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