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CAT 2017 Slot 1 — QA Question 12

DiscountEasy

If Fatima sells 60 identical toys at a 40% discount on the printed price, then she makes 20% profit. Ten of these toys are destroyed in fire. While selling the rest, how much discount should be given on the printed price so that she can make the same amount of profit?

Answer & solution

Correct answer: 28%

  • A

    30%

  • B

    25%

  • C

    24%

  • 28%

Solution

Medium

Let printed price =p=p. From the 6060-toy sale (40%40\% discount, 20%20\% profit) back out the cost price and the actual rupee profit. After the fire only 5050 toys remain; find the selling price that yields the same rupee profit, then convert to a discount %\%.

1

Revenue and cost for 6060 toys. At 40%40\% discount each toy sells for 0.6p0.6p.

SP60=60×0.6p=36p⇒ CP=36p1.2=30p(20% profit)\begin{aligned} &\text{SP}_{60} = 60\times 0.6p = 36p\\ &\Rightarrow\ \text{CP} = \frac{36p}{1.2} = 30p \quad\text{(}20\%\text{ profit)} \end{aligned}
2

Profit in rupees. The 20%20\% profit on cost 30p30p.

profit=0.2×30p=6p\begin{aligned} &\text{profit} = 0.2\times 30p = 6p \end{aligned}
3

Target revenue from the 5050 surviving toys. Same rupee profit 6p6p over the same total cost 30p30p.

SP50=CP+profit=30p+6p=36p\begin{aligned} &\text{SP}_{50} = \text{CP} + \text{profit} = 30p + 6p = 36p \end{aligned}
4

Discount needed. 5050 toys at printed price would fetch 50p50p; the discount is the shortfall.

discount=50p−36p=14p⇒ 14p50p×100%=28%\begin{aligned} &\text{discount} = 50p - 36p = 14p\\ &\Rightarrow\ \frac{14p}{50p}\times 100\% = 28\% \end{aligned}
28%28\%

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CAT 2017 Slot 1 QA Q12: If Fatima sells 60 identical toys at a 40% discount on the printed price, then she makes 20% profit. Ten of th — Solution | TheCATExam