CAT 2019 Slot 2 QA Question & Solution
Question
Mukesh purchased 10 bicycles in 2017, all at the same price. He sold six of these at a profit of 25% and the remaining four at a loss of 25%. If he made a total profit of Rs. 2000, then his purchase price of a bicycle, in Rupees, was
Options
Solution
Let the cost of each bicycle $= 100b$.
Hence, the cost price (CP) of 10 bicycles $= 1000b$.
It is given that six bicycles are sold at a profit of 25% and the remaining four are sold at a loss of 25%.
So, the selling price (SP) of the 10 bicycles is:
$$
\text{SP} = 125b \times 6 + 75b \times 4
$$
$$
\text{SP} = 750b + 300b = 1050b
$$
The total profit is:
$$
\text{Profit} = \text{SP} - \text{CP} = 1050b - 1000b = 50b
$$
It is given that this profit corresponds to 2000, so:
$$
50b = 2000 \implies b = 40
$$
Hence, the cost of one bicycle:
$$
\text{CP} = 100b = 100 \times 40 = 4000
$$
Therefore, the cost price of each bicycle is 4000.