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CAT 2021 Slot 2 — QA Question 3

Profit & LossEasy

A person buys tea of three different qualities at ₹ 800, ₹ 500, and ₹ 300 per kg, respectively, and the amounts bought are in the proportion 2 : 3 : 5. She mixes all the tea and sells one-sixth of the mixture at ₹ 700 per kg. The price, in INR per kg, at which she should sell the remaining tea, to make an overall profit of 50%, is 

Answer & solution

  • A

    692

  • 688

  • C

    675

  • D

    653

Solution

Easy

Pick a convenient batch of 2:3:52{:}3{:}5 kg, get the total cost, mark the required overall selling price up by 50%50\%, subtract the revenue from the one-sixth already sold, then divide by the remaining weight.

1

Choose quantities and find total cost. Take 2,3,52,3,5 kg of the three qualities (1010 kg total).

Cost=2(800)+3(500)+5(300)⇒ Cost=1600+1500+1500=₹4600\begin{aligned} &\text{Cost}=2(800)+3(500)+5(300)\\ &\Rightarrow\ \text{Cost}=1600+1500+1500=\text{₹}4600 \end{aligned}
2

Required total revenue for 50%50\% profit.

SPtotal=4600×1.5=₹6900\begin{aligned} &\text{SP}_{\text{total}}=4600\times 1.5=\text{₹}6900 \end{aligned}
3

Revenue from the one-sixth sold at ₹700. One-sixth of 1010 kg is 106\tfrac{10}{6} kg.

SP1/6=106×700=70006 ₹\begin{aligned} &\text{SP}_{1/6}=\tfrac{10}{6}\times 700=\tfrac{7000}{6}\ \text{₹} \end{aligned}
4

Price for the remaining 506\tfrac{50}{6} kg. Subtract the revenue already earned, then divide by the leftover weight.

SPrest=6900−70006=41400−70006=344006 ₹⇒ rate=344006÷506=3440050=688\begin{aligned} &\text{SP}_{\text{rest}}=6900-\tfrac{7000}{6}=\tfrac{41400-7000}{6}=\tfrac{34400}{6}\ \text{₹}\\ &\Rightarrow\ \text{rate}=\tfrac{34400}{6}\div\tfrac{50}{6}=\tfrac{34400}{50}=688 \end{aligned}
Selling rate of remaining tea=₹688 per kg\text{Selling rate of remaining tea}=\text{₹}688\text{ per kg}
CAT 2021 Slot 2 QA Q3: A person buys tea of three different qualities at ₹ 800, ₹ 500, and ₹ 300 per kg, respectively, and the amount — Solution | TheCATExam