CAT 2019Slot 2QAQuestion & 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
6000
8000
4000
2000
Solution
1. Concept Used
- Topic: Profit and Loss — Net Profit Calculation
- Formula: $$\text{Net Profit} = \text{Total SP} - \text{Total CP}$$
2. Calculation
Let the cost price of each bicycle be $$x$$ Rupees.
Total cost price of all 10 bicycles: $$\text{Total CP} = 10x$$
Six bicycles sold at a profit of 25%: $$\text{SP of each} = x \times \frac{125}{100} = 1.25x$$ $$\text{SP of 6 bicycles} = 6 \times 1.25x = 7.5x$$
Remaining four bicycles sold at a loss of 25%: $$\text{SP of each} = x \times \frac{75}{100} = 0.75x$$ $$\text{SP of 4 bicycles} = 4 \times 0.75x = 3x$$
Total Selling Price: $$\text{Total SP} = 7.5x + 3x = 10.5x$$
Net Profit: $$\text{Profit} = \text{Total SP} - \text{Total CP} = 10.5x - 10x = 0.5x$$
We are told the total profit is Rs. 2000: $$0.5x = 2000$$ $$x = \frac{2000}{0.5} = 4000$$
The key insight here is that selling 6 out of 10 at +25% and 4 at −25% does not break even — the positive side carries more weight (6 items vs 4 items), resulting in a net gain of 5% of Total CP, i.e., $$0.5x$$.
3. Solution
Answer = Option 3 ✅
The purchase price of each bicycle is Rs. 4000.