A shopkeeper buys shirts from a producer and sells them at 20% profit. A customer has to pay Rs. 3,186.00 including 18% taxes, per shirt. At what price did the shopkeeper buy each shirt from the producer?
Rs. 2,500.00
Rs. 1,975.40
Rs. 2,250.00
Rs. 2,548.80
ANSWER
The shopkeeper bought each shirt for Rs. 2,250.00, option (C).
Official answer: CSource: Official answer key, GATE 2024 EE (IISc Bengaluru)
Let the shopkeeper's cost price be . A 20% profit on cost makes the selling price before tax .
The 18% tax is charged on that selling price, so the customer pays .
Successive percentage increases multiply:
Undo the tax first: . So the shopkeeper's selling price before tax is Rs. 2,700.
Then undo the profit: . So the cost price is Rs. 2,250.
Check: and . Each shirt cost the shopkeeper Rs. 2,250.00, which is option (C).
KEY IDEA
Profit and tax are successive percentage increases, so their multipliers multiply: final price cost cost. To go back to the cost, divide by each multiplier in reverse order (tax first, then profit). Never subtract the percentages from the final price.
WATCH OUT FOR
Removing the percentages from the final price as if they were shares of it. For example, taking 20% off Rs. 3,186 gives , which is option (D). That treats the profit as 20% of the price the customer paid, when it is 20% of the cost, and it forgets the tax completely. A 20% markup is undone by dividing by 1.2, not by multiplying by 0.8, and the 18% tax is undone by dividing by 1.18.
From the GATE 2024 EE paper. Every question of this paper · Download the full paper · All 58 Numerical questions, with notes
