TheCATExam
Sign in

CAT 2022 Slot 1 — QA Question 1

DiscountEasy

Ankita buys 4 kg cashews, 14 kg peanuts and 6 kg almonds when the cost of 7 kg cashews is the same as that of 30 kg peanuts or 9 kg almonds. She mixes all the three nuts and marks a price for the mixture in order to make a profit of ₹1752. She sells 4 kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of ₹744. Then the amount, in rupees, that she had spent in buying almonds is

Answer & solution

  • A

    1176

  • 1680

  • C

    2520

  • D

    1440

Solution

Easy

Use the equal-cost condition 7c=30p=9a7c=30p=9a to get the per-kg price ratio of cashews, peanuts and almonds. Build the cost of the 2424 kg mixture, fix the per-kg marked profit from the planned \unicodex20B91752\unicode{x20B9}1752, then use the actual profit \unicodex20B9744\unicode{x20B9}744 (with a 20%20\% discount on 2020 kg) to pin down the scale and finally the almond spend.

1

Turn the equal-cost line into a price ratio. Let prices per kg be c,p,ac,p,a:

7c=30p=9a=LCM(7,30,9) x=630x⇒ c=90x,p=21x,a=70x\begin{aligned} &7c=30p=9a=\text{LCM}(7,30,9)\,x=630x\\ &\Rightarrow\ c=90x,\quad p=21x,\quad a=70x \end{aligned}
2

Cost of the full 2424 kg mixture (4 kg cashews + 14 kg peanuts + 6 kg almonds):

CP=4(90x)+14(21x)+6(70x)=360x+294x+420x=1074x⇒ CP per kg=1074x24=44.75x\begin{aligned} &\text{CP}=4(90x)+14(21x)+6(70x)=360x+294x+420x=1074x\\ &\Rightarrow\ \text{CP per kg}=\frac{1074x}{24}=44.75x \end{aligned}
3

Marked price = planned profit of \unicodex20B91752\unicode{x20B9}1752. That is a per-kg profit of

175224=\unicodex20B973 per kg at the marked price.\frac{1752}{24}=\unicode{x20B9}73\text{ per kg at the marked price.}

So the 44 kg sold at the marked price earn a profit of 4×73=\unicodex20B92924\times73=\unicode{x20B9}292.

4

The remaining 2020 kg (sold at 20%20\% off) must make up the rest of the actual \unicodex20B9744\unicode{x20B9}744 profit:

profit needed on 20 kg=744−292=\unicodex20B9452CP of 20 kg=20×44.75x=895xmarked SP of 20 kg=895x+20×73⏟1460 (planned profit)\begin{aligned} &\text{profit needed on }20\text{ kg}=744-292=\unicode{x20B9}452\\ &\text{CP of }20\text{ kg}=20\times44.75x=895x\\ &\text{marked SP of }20\text{ kg}=895x+\underbrace{20\times73}_{1460}\ (\text{planned profit}) \end{aligned}
5

Apply the 20%20\% discount and equate to the actual profit, then solve for xx:

0.8 (895x+1460)=895x+4521460(0.8)−452=895x(0.2)716=179x ⇒ x=4\begin{aligned} &0.8\,(895x+1460)=895x+452\\ &1460(0.8)-452=895x(0.2)\\ &716=179x\ \Rightarrow\ x=4 \end{aligned}
6

Amount spent on almonds = 66 kg at a=70xa=70x:

6×70x=6×70×4=\unicodex20B916806\times70x=6\times70\times4=\unicode{x20B9}1680
\unicodex20B9 1680\unicode{x20B9}\,\mathbf{1680}
CAT 2022 Slot 1 QA Q1: Ankita buys 4 kg cashews, 14 kg peanuts and 6 kg almonds when the cost of 7 kg cashews is the same as that of — Solution | TheCATExam