Profit and Loss Question 2 - CAT 2023
Gita sells two objects A and B at the same price such that she makes a profit of 20% on object A and a loss of 10% on object B. If she increases the selling price such that objects A and B are still sold at an equal price and a profit of 10% is made on object B, then the profit made on object A will be nearest to:
Step-by-Step Explanation
Let the initial equal selling price of objects A and B be p.
- Determine Cost Prices:
Object A is sold at a 20% profit:
1.20 × CPₐ = p
CPₐ = p / 1.20 = 5p / 6
Object B is sold at a 10% loss:
0.90 × CPᵦ = p
CPᵦ = p / 0.90 = 10p / 9
- Analyze the New Scenario:
The new selling price s is identical for both objects, and a 10% profit is realized on object B:
s = 1.10 × CPᵦ
s = 1.10 × 10p / 9 = 11p / 9
- Calculate New Profit Percentage on Object A:
Profit on A = (s − CPₐ) / CPₐ × 100
= ((11p / 9) / (5p / 6) − 1) × 100
Ratio of SP to CP for A = (11 / 9) × (6 / 5) = 22 / 15
Profit Percentage = (22 / 15 − 1) × 100
= 7 / 15 × 100
≈ 46.66%
The value nearest to 46.66% among the choices is 47%.
Correct Option: C
💡 FundaMakers Tip:
When a question contains only percentages and ratios without fixed values, assume a smart number instead of dragging variables like p.
Look at the denominators for the cost prices: 6 and 9. Their LCM is 18. Let the initial selling price be Rs. 90 (a multiple of 18).
CPₐ = 90 / 1.2 = 75
CPᵦ = 90 / 0.9 = 100
New SP = 1.1 × 100 = 110
New Profit on A = (110 − 75) / 75 × 100 = 35 / 75 × 100 = 46.66%.
Assuming a smart value clears the algebra out of your way instantly.