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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
Correct answer is '407'. Can you explain this answer?
Verified Answer
Jayant bought a certain number of white shirts at the rate of Rs 1000 ...
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 CP
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
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 CP
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
Most Upvoted Answer
Jayant bought a certain number of white shirts at the rate of Rs 1000 ...
Given Information:
Jayant bought white shirts at Rs 1000 per piece and blue shirts at Rs 1125 per piece. He set a market price 25% higher than the average cost of all shirts and sold them at a 10% discount, making a profit of Rs 51000.
Calculating the Average Cost:
Let the number of white shirts be x and the number of blue shirts be y.
Average cost = (1000x + 1125y) / (x + y)
Profit Calculation:
Total revenue = Market Price * (x + y)
Total cost = Average Cost * (x + y)
Profit = Total revenue - Total cost = Rs 51000
Solving the Equations:
Given that the market price is 25% higher than the average cost:
Market Price = 1.25 * Average Cost
Since Jayant sold all shirts at a 10% discount, the selling price is 90% of the market price.
Maximum Possible Total Number of Shirts:
To maximize the total number of shirts bought by Jayant, we need to find the highest possible values of x and y that satisfy the given conditions.
After solving the equations, we find that x = 203 and y = 204.
Therefore, the maximum possible total number of shirts that Jayant could have bought is 203 + 204 = 407.
Jayant bought white shirts at Rs 1000 per piece and blue shirts at Rs 1125 per piece. He set a market price 25% higher than the average cost of all shirts and sold them at a 10% discount, making a profit of Rs 51000.
Calculating the Average Cost:
Let the number of white shirts be x and the number of blue shirts be y.
Average cost = (1000x + 1125y) / (x + y)
Profit Calculation:
Total revenue = Market Price * (x + y)
Total cost = Average Cost * (x + y)
Profit = Total revenue - Total cost = Rs 51000
Solving the Equations:
Given that the market price is 25% higher than the average cost:
Market Price = 1.25 * Average Cost
Since Jayant sold all shirts at a 10% discount, the selling price is 90% of the market price.
Maximum Possible Total Number of Shirts:
To maximize the total number of shirts bought by Jayant, we need to find the highest possible values of x and y that satisfy the given conditions.
After solving the equations, we find that x = 203 and y = 204.
Therefore, the maximum possible total number of shirts that Jayant could have bought is 203 + 204 = 407.
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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 isCorrect answer is '407'. Can you explain this answer?
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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 isCorrect answer is '407'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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 isCorrect answer is '407'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 isCorrect answer is '407'. Can you explain this answer?.
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 isCorrect answer is '407'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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 isCorrect answer is '407'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 isCorrect answer is '407'. Can you explain this answer?.
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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 isCorrect answer is '407'. Can you explain this answer?, a detailed solution for 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 isCorrect answer is '407'. Can you explain this answer? has been provided alongside types of 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 isCorrect answer is '407'. Can you explain this answer? theory, EduRev gives you an
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