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CAT 2020 Slot 3 — QA Question 12

DiscountEasy

A man buys 35 kg of sugar and sets a marked price in order to make a 20% profit. He sells 5 kg at this price, and 15 kg at a 10% discount. Accidentally, 3 kg of sugar is wasted. He sells the remaining sugar by raising the marked price by p percent so as to make an overall profit of 15%. Then p is nearest to

Answer & solution

  • 25

  • B

    35

  • C

    22

  • D

    31

Solution

Medium

Fix a convenient cost price per kg, find the marked price from the desired 20\% profit, then equate the total revenue from all four lots to the revenue needed for an overall 15\% profit and solve for the extra mark-up pp.

1

Set cost and marked price. Take the cost price as $100\$100 per kg. A 20%20\% mark-up gives the marked price.

MP=100×1.20=120 per kg⇒ Total cost=35×100=3500(35 kg bought)\begin{aligned} &\text{MP}=100\times 1.20=120\ \text{per kg}\\ &\Rightarrow\ \text{Total cost}=35\times 100=3500 \quad\text{(35 kg bought)} \end{aligned}
2

Revenue needed for a 15\% overall profit.

Required revenue=3500×1.15=4025\begin{aligned} &\text{Required revenue}=3500\times 1.15=4025 \end{aligned}
3

Revenue from the first three lots. 55 kg at MP, 1515 kg at 10%10\% discount, and 33 kg wasted (sold for nothing).

5×120=60015×120×0.90=16203×0=0\begin{aligned} &5\times 120=600\\ &15\times 120\times 0.90=1620\\ &3\times 0=0 \end{aligned}
4

Remaining sugar and the new mark-up. Sugar left =35−5−15−3=12=35-5-15-3=12 kg, sold at the marked price raised by p%p\%.

Revenue=12×120×(1+p100)=1440(1+p100)\begin{aligned} &\text{Revenue}=12\times 120\times\left(1+\tfrac{p}{100}\right)=1440\left(1+\tfrac{p}{100}\right) \end{aligned}
5

Equate total revenue to the required revenue and solve.

600+1620+0+1440(1+p100)=4025(steps 2–4)⇒ 1440(1+p100)=1805⇒ 1+p100=18051440≈1.2535⇒ p≈25.3\begin{aligned} &600+1620+0+1440\left(1+\tfrac{p}{100}\right)=4025 \quad\text{(steps 2–4)}\\ &\Rightarrow\ 1440\left(1+\tfrac{p}{100}\right)=1805\\ &\Rightarrow\ 1+\tfrac{p}{100}=\frac{1805}{1440}\approx 1.2535\\ &\Rightarrow\ p\approx 25.3 \end{aligned}
p≈25p\approx 25
CAT 2020 Slot 3 QA Q12: A man buys 35 kg of sugar and sets a marked price in order to make a 20% profit. He sells 5 kg at this price, — Solution | TheCATExam