TheCATExam
Sign in

CAT 2020 Slot 2 — QA Question 25

DiscountEasy

Anil buys 12 toys and labels each with the same selling price. He sells 8 toys initially at 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

Answer & solution

  • 50

  • B

    54

  • C

    60

  • D

    55

Solution

Easy

Write the total revenue in terms of the labeled (marked) price mm to find mm. Separately, the 10%10\% overall profit ties the total cost to the 21122112 revenue, giving the cost per toy. The "no-discount" profit then compares the full label mm against cost.

1

Set up revenue in terms of mm. Each toy is labeled mm. The first 8 sell at 20%20\% off (factor 0.80.8); the last 4 take a further 25%25\% off (factor 0.75×0.80.75\times0.8).

Rev=8(0.8m)+4(0.75×0.8 m)⇒ Rev=6.4m+2.4m=8.8m\begin{aligned} &\text{Rev}=8(0.8m)+4(0.75\times0.8\,m)\\ &\Rightarrow\ \text{Rev}=6.4m+2.4m=8.8m \end{aligned}
2

Solve for the label mm. Total revenue is 21122112:

8.8m=2112(from step 1)⇒ m=240\begin{aligned} &8.8m=2112 \quad\text{(from step 1)}\\ &\Rightarrow\ m=240 \end{aligned}
3

Find the cost per toy. The 21122112 already includes a 10%10\% profit over total cost 12c12c:

12c×1.1=2112⇒ 13.2 c=2112⇒ c=160\begin{aligned} &12c\times 1.1=2112\\ &\Rightarrow\ 13.2\,c=2112\\ &\Rightarrow\ c=160 \end{aligned}
4

No-discount profit. Selling every toy at the full label m=240m=240 against cost c=160c=160:

Profit%=m−cc×100=240−160160×100⇒ =80160×100=50%\begin{aligned} &\text{Profit}\%=\frac{m-c}{c}\times 100=\frac{240-160}{160}\times 100\\ &\Rightarrow\ =\frac{80}{160}\times 100=50\% \end{aligned}
50%50\%
CAT 2020 Slot 2 QA Q25: Anil buys 12 toys and labels each with the same selling price. He sells 8 toys initially at 20% discount on th — Solution | TheCATExam