Combined price of large and small shirts

CAT 2021 Slot 3 · QA · Hard · Linear Equations

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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

  1. A.

    150

  2. B.

    225

  3. C.

    175

  4. D.

    200

Answer

D

Explanation

Let price of a large shirt be pp, small shirt be p−50p - 50. Number of large shirts = 5000p\frac{5000}{p}, small shirts = 1800p−50\frac{1800}{p - 50}.

Total shirts = 64: 5000p+1800p−50=64\frac{5000}{p} + \frac{1800}{p - 50} = 64

Divide by 8: 625p−50+625−625p…\frac{625}{p - 50} + \frac{625 - 625}{p} \dots 625(p−50)+225pp(p−50)=8\frac{625(p-50) + 225p}{p(p-50)} = 8 850p−31250=8p2−400p850p - 31250 = 8p^2 - 400p 8p2−1250p+31250=0  ⟹  4p2−625p+15625=08p^2 - 1250p + 31250 = 0 \implies 4p^2 - 625p + 15625 = 0 (p−125)(4p−125)=0(p - 125)(4p - 125) = 0

If p=125p = 125, price of small shirt = 7575. Price of large and small shirt together = 125+75=200125 + 75 = 200.

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