CAT 2023 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like **Speed-time-distance**, **Mixture and Alligations**. This year, there was a surprise. The questions from **Geometry** were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 15 : 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

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Let the number of white and black shirts bought by Jayant be w and b respectively.

Then the total Cost Price (CP) \( = 1000 \times w + 1125 \times b = 1000 ( w + b ) + 125 \times b \)

Since the goods are marked up by 25% and then offered at a discount of 10%, the total Selling Price (SP) \( = C P \times 1.25 \times 0.9 = 1.125 C P \)

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

\( 1000 ( w + b ) + 125 \times b = 4,08,000 \)

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 \( 1000 ( w + b ) + 125 \times b = 4,08,000 \).

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

The question is **" 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 " **

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