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CAT 2017 Slot 1 — QA Question 6

DiscountEasy

If a seller gives a discount of 15% on retail price, she still makes a profit of 2%. Which of the following ensures that she makes a profit of 20%?

Answer & solution

Correct answer: Sell at retail price

  • A

    Give a discount of 5% on retail price

  • B

    Give a discount of 2% on retail price

  • C

    Increase the retail price by 2%

  • Sell at retail price

Solution

Easy

Anchor the retail price at 100100. Use the given "15%15\% discount → 2%2\% profit" to back out the cost price, then find what selling price gives 20%20\% profit and compare it to the options.

1

Selling price with the known discount. Let retail price (MRP) =100=100.

SP=100−15% of 100=85\begin{aligned} &\text{SP} = 100 - 15\% \text{ of }100 = 85 \end{aligned}
2

Recover the cost price. That 8585 already includes a 2%2\% profit.

CP×1.02=85⇒ CP=851.02=5006≈83.33\begin{aligned} &\text{CP}\times 1.02 = 85\\ &\Rightarrow\ \text{CP} = \frac{85}{1.02} = \frac{500}{6}\approx 83.33 \end{aligned}
3

Selling price for 20%20\% profit. Multiply CP by 1.21.2.

SP20%=5006×1.2=5006×65⇒ SP20%=100=MRP\begin{aligned} &\text{SP}_{20\%} = \frac{500}{6}\times 1.2 = \frac{500}{6}\times\frac{6}{5}\\ &\Rightarrow\ \text{SP}_{20\%} = 100 = \text{MRP} \end{aligned}

So she must sell at the full retail price (zero discount) — this matches the last option, while 5%5\%/2%2\% discounts or a 2%2\% price hike all fall short.

Sell at retail price\textbf{Sell at retail price}

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CAT 2017 Slot 1 QA Q6: If a seller gives a discount of 15% on retail price, she still makes a profit of 2%. Which of the following en — Solution | TheCATExam