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

The Correct Option is D

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): \(200\)