CAT 2021 Slot 3 QA Q15 Equations

Question 15 of the Quantitative Ability (QA) section, CAT 2021 Slot 3, with CAT's official answer and a worked solution.

A shop owner bought a total of 64 shirts from a wholesale market that came in two sizes, small and large. The price of a small shirt was INR 50 less than that of a large shirt. She paid a total of INR 5000 for the large shirts, and a total of INR 1800 for the small shirts. Then, the price of a large shirt and a small shirt together, in INR, is

A
150
B
225
C
175
D
200

Answer: (D) 200 Equations MCQ

Solution

Let a large shirt cost \(p\), small \(p - 50\). Then \(\frac{5000}{p} + \frac{1800}{p - 50} = 64\).
Options give \(2p - 50\), so try \(p = 125\): \(40 + \frac{1800}{75} = 40 + 24 = 64\). Correct.
Large + small \(= 125 + 75 = 200\).

Shortcut. Plug options: \(p = \frac{\text{option} + 50}{2}\) must divide 5000 nicely.