CAT 2023 Question Paper | Quant Slot 3

CAT 2023 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 11 : 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

Video Explanation

Explanatory Answer

Let's say the merchant paid for \( 95 \times 100 \mathrm {~m} \).
He pays \( 95 \times 100 \times 100 \)rupees and gets \( 95 \times 105 \mathrm {~m} \)of cloth.
(because, he pays Rs. 100/meter and gets 5% extra cloth)
He sells 95 cm of the cloth at Rs. 104.5 (5% discounted on Rs. 110)
So, the total money collected by the merchant will be \( 104.5 \times \frac { 95 \times 105 \mathrm {~m} } { 95 \sim \mathrm { cm } } = 104.5 \times \frac { 95 \times 105 \sim m } { 0.95 \sim m } = 104.5 \times 100 \times 105 \)
\( \frac { \text { Money collected } } { \text { Money Paid } } = \frac { 104.5 \times 100 \times 105 } { 95 \times 100 \times 100 } = 1.155 \)
This means, the profit percentage is 15.5%
Observe that the initial number chosen for the length of the cloth is such that the calculations are easy. As you practice more of these questions, you should be able to write a single equation like \( \frac { 1.05 \times 1.1 \times 0.95 } { 0.95 } = 1.155 \)

The question is " 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 "

The answer is '15.5%'

Choice B is the correct answer.