CAT 2021 Slot 3 · Quant · Question 15

Let a small shirt cost y, so a large one costs y+50.

The counts come from the totals spent: \frac{1800}{y} small shirts and \frac{5000}{y+50} large ones, and together they make 64:

\frac{1800}{y}+\frac{5000}{y+50}=64.

Clearing denominators gives 1800\left( y+50 \right)+5000y=64y\left( y+50 \right), that is 6800y+90000=64{y}^{2}+3200y, so 64{y}^{2}-3600y-90000=0, or 4{y}^{2}-225y-5625=0.

Factorising, \left( y-75 \right)\left( 4y+75 \right)=0, and a price is positive, so y=75.

The small shirt costs ₹75 and the large one ₹125 (giving 24 and 40 shirts, which is 64). Together they cost ₹200.