TheCATExam
Sign in

CAT 2023 Slot 3 — QA Question 8

Dishonest MerchantEasy

A merchant purchases a cloth at a rate of Rs.100 per meter and receives 5 cm length of cloth free for every 100 cm length of cloth purchased by him. He sells the same cloth at a rate of Rs.110 per meter but cheats his customers by giving 95 cm length of cloth for every 100 cm length of cloth purchased by the customers. If the merchant provides a 5% discount, the resulting profit earned by him is

Answer & solution

  • A

    9.7%

  • B

    4.2%

  • 15.5%

  • D

    16%

Solution

Easy

Track profit as a product of multiplying factors. Profit comes from three places: the price markup, the discount, and the two length-cheats (extra cloth received while buying, short cloth given while selling). Multiply all the factors; the overall factor minus 11 is the profit fraction.

1

Price factor (sells at Rs.110 vs cost Rs.100, then a 5% discount):

110100×0.95\frac{110}{100}\times 0.95
2

Quantity factor. Buying: he pays for 100100 cm but receives 105105 cm ⇒105100\Rightarrow \frac{105}{100}. Selling: he charges for 100100 cm but hands over only 9595 cm ⇒10095\Rightarrow \frac{100}{95}. Combined:

105100×10095=10595\frac{105}{100}\times\frac{100}{95}=\frac{105}{95}
3

Multiply everything for the overall factor:

factor=110100×0.95×10595=1110×0.95×10595=1110×105100=1.155\begin{aligned} \text{factor}&=\frac{110}{100}\times 0.95\times\frac{105}{95}\\ &=\frac{11}{10}\times\frac{0.95\times105}{95}\\ &=\frac{11}{10}\times\frac{105}{100}=1.155 \end{aligned}
4

Convert to profit percent:

(1.155−1)×100%=15.5%(1.155-1)\times 100\%=15.5\%

Resulting profit =15.5%=\mathbf{15.5\%}.

The discount 0.950.95 and the buying-bonus tail cancel neatly: 0.95×10595=1051000.95\times\frac{105}{95}=\frac{105}{100}. So the factor is just 1110×105100=1.155\frac{11}{10}\times\frac{105}{100}=1.155 — no messy arithmetic.

CAT 2023 Slot 3 QA Q8: A merchant purchases a cloth at a rate of Rs.100 per meter and receives 5 cm length of cloth free for every 10 — Solution | TheCATExam