Profit and Loss Question 4 - CAT 2020
Anil buys 12 toys and labels each with the same selling price. He sells 8 toys initially at a 20% discount on the labeled price. Then he sells the remaining 4 toys at an additional 25% discount on the discounted price. Thus, he gets a total of Rs. 2112, and makes a 10% profit. With no discounts, his percentage of profit would have been:
Step-by-Step Explanation
Let the labeled (marked) price of a single toy be L.
- 8 toys are sold at a 20% discount → 8 × 0.80L = 6.4L.
- The remaining 4 toys are sold at an additional 25% discount on the already discounted price (0.80L × 0.75 = 0.60L) → 4 × 0.60L = 2.4L.
Total accumulated selling price in terms of L:
Total SP = 6.4L + 2.4L = 8.8L
We are given that this total SP equals Rs. 2112:
8.8L = 2112
L = 2112 / 8.8 = 240
The total transaction yielded a 10% net profit on the total cost price (CP):
Total CP = 2112 / 1.10 = 1920
If no discounts were given, all 12 toys would be sold at the full labeled price L = 240:
Undiscounted SP = 12 × 240 = 2880
Profit Percentage = [(2880 − 1920) / 1920] × 100
= (960 / 1920) × 100
= 50%
Correct Option: A
💡 FundaMakers Tip:
You can bypass calculating the absolute currency values entirely to save time.
We established that the discounted total SP is 8.8L, which corresponds to a 1.10 × CP value.
The undiscounted total SP is exactly 12L.
Using a simple ratio comparison:
New SP Factor = 1.10 × 12 / 8.8 = 1.50 × CP.
A multiplier of 1.50 translates directly to a 50% profit margin, completely avoiding the need to process the number 2112.