Question

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 1

Answer: (D)

200

Answer 2

Let number of small shirts be $x$ and price of a small shirt be $y$.
Then number of large shirts be $(64 - x)$ and the price of a large shirt becomes $(y + 50)$
Total Money spent on small shirts,
$xy = 1800$
Total money spent on large shirts,
$(64 - x) (y + 50) = 5000$
$(64 - x) (y + 50) = 5000$
$64y + 3200 - xy - 50x = 5000$
$64y + 3200 - 1800 - 50x = 5000$
$64y + 1400 - 50x = 5000$
$64y - 50x = 3600$
$32y - 25x = 1800$
32y - 25$$($$\frac{1800}{y}) $= 1800$
$32y^2 - 1800y - 25(1800) = 0$
$4y^2 - 9(25)y - 25(9)(25) = 0$
$y = 75$
Price of a small shirt $= y= 75$
Price of a small shirt $= y + 50 = 125$
The Total price of a large shirt and a small shirt,
$= 75 + 125$
$= 200$

So, the correct option is (D): $200$