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
Explanation:
Let the price of a smaller shirt be Rs. p. Hence, price of a larger shirt will be Rs. (p + 50).
⇒ 5000p+50 + 1800p = 64
⇒ 6800p + 90000 = 64p2 + 3200p
⇒ 4p2 - 225p - 5625 = 0
⇒ 4p2 - 300p + 75p - 5625 = 0
⇒ (4p + 75)(p - 75) = 0
⇒ p = 75 or -75/4 (rejected)
⇒ Price of a smaller and a larger shirt = 75 + (75 + 50) = 200
Hence, option (b).
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