Jayant bought a certain number of white shirts at the rate of Rs 1000 per piece and a certain number of blue shirts at the rate of Rs 1125 per piece. For each shirt, he then set a fixed market price which was 25% higher than the average cost of all the shirts. He sold all the shirts at a discount of 10% and made a total profit of Rs 51000. If he bought both colors of shirts, then the maximum possible total number of shirts that he could have bought is
Started 1 month ago by Shashank in
Explanatory Answer
Let the number of white and black shirts bought by Jayant be w and b respectively.
Then the total Cost Price (CP) =1000×w+1125×b=1000(w+b)+125×b
Since the goods are marked up by 25% and then offered at a discount of 10%, the total Selling
Price (SP) =CP×1.25×0.9=1.125
This implies that there was a 12.5% of Profit, which is given to be 51, 000
12.5%(CP) = 51,000
CP = 4,08,000
1000(w+b)+125×b=4,08,000
w and b are positive integers (since at least one shirt of each color needs to be purchased.)
To purchase maximum number of shirts, you need to purchase minimum number of the costlier shirts, which are the blue ones
Observe that the total CP is a multiple of 1000. And for that to happen b should be a multiple of 8 in 1000(w+b)+125×b=4,08,000
So the minimum value of b = 8, in which case, w = 399. Hence, the maximum number of shirts
that can be purchased = 399 + 8 = 407
-
No one is replied to this question yet. Be first to reply!
