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The cost price of 10 shirts and 5 trousers together is Rs. 10,000, A shopkeeper sells shirts at a profit of 15% and trousers at a loss of 10% and his overall gain is Rs. 275. Find the cost price of a shirt.
Correct answer is '510'. Can you explain this answer?
Most Upvoted Answer
The cost price of 10 shirts and 5 trousers together is Rs. 10,000, A s...
Given
The cost price of 10 shirts and 5 trousers together = Rs. 10,000
A shopkeeper sells shirts at a profit of 15% and trousers at a loss of 10% and his overall gain = Rs. 275
Formula Used
Profit% = (Profit/CP) × 100
Loss% = (Loss/CP) × 100
Calculation
Let the cost price of shirt and trouser be x and y
According to the question
10x + 5y = 10000 ----(1)
And also according to the question
10x (15/100) - 5y (10/100) = 275
⇒ 15x - 5y = 2750 ---(2)
On adding (1) and (2), we get
25x = 12750
⇒ x = 510
∴ The cost price of a shirt is Rs. 510.
Community Answer
The cost price of 10 shirts and 5 trousers together is Rs. 10,000, A s...
Given Information:
- Cost price of 10 shirts + 5 trousers = Rs. 10,000
- Selling price of shirts has a profit of 15%
- Selling price of trousers has a loss of 10%
- Overall gain = Rs. 275
Let's assume:
- Cost price of each shirt = Rs. X
- Cost price of each trouser = Rs. Y
Calculating the Selling Price:
- Selling price of each shirt = Cost price of shirt + Profit
= X + (15/100)X
= X + 0.15X
= 1.15X
- Selling price of each trouser = Cost price of trouser - Loss
= Y - (10/100)Y
= Y - 0.1Y
= 0.9Y
Calculating the Total Selling Price:
- Total selling price of 10 shirts = 10 * Selling price of each shirt
= 10 * 1.15X
= 11.5X
- Total selling price of 5 trousers = 5 * Selling price of each trouser
= 5 * 0.9Y
= 4.5Y
- Total selling price of 10 shirts + 5 trousers = Rs. 10,000
=> 11.5X + 4.5Y = 10,000 ---(1)
Calculating the Overall Gain:
- Overall gain = Total selling price - Total cost price
= (10 shirts + 5 trousers) - (10X + 5Y)
= 11.5X + 4.5Y - (10X + 5Y)
= 1.5X - 0.5Y
Given that the overall gain is Rs. 275, we have:
1.5X - 0.5Y = 275 ---(2)
Solving the Equations:
From equations (1) and (2), we have the following system of equations:
11.5X + 4.5Y = 10,000 ---(1)
1.5X - 0.5Y = 275 ---(2)
Solving these equations, we get:
X = 510
Therefore, the cost price of a shirt is Rs. 510.
- Cost price of 10 shirts + 5 trousers = Rs. 10,000
- Selling price of shirts has a profit of 15%
- Selling price of trousers has a loss of 10%
- Overall gain = Rs. 275
Let's assume:
- Cost price of each shirt = Rs. X
- Cost price of each trouser = Rs. Y
Calculating the Selling Price:
- Selling price of each shirt = Cost price of shirt + Profit
= X + (15/100)X
= X + 0.15X
= 1.15X
- Selling price of each trouser = Cost price of trouser - Loss
= Y - (10/100)Y
= Y - 0.1Y
= 0.9Y
Calculating the Total Selling Price:
- Total selling price of 10 shirts = 10 * Selling price of each shirt
= 10 * 1.15X
= 11.5X
- Total selling price of 5 trousers = 5 * Selling price of each trouser
= 5 * 0.9Y
= 4.5Y
- Total selling price of 10 shirts + 5 trousers = Rs. 10,000
=> 11.5X + 4.5Y = 10,000 ---(1)
Calculating the Overall Gain:
- Overall gain = Total selling price - Total cost price
= (10 shirts + 5 trousers) - (10X + 5Y)
= 11.5X + 4.5Y - (10X + 5Y)
= 1.5X - 0.5Y
Given that the overall gain is Rs. 275, we have:
1.5X - 0.5Y = 275 ---(2)
Solving the Equations:
From equations (1) and (2), we have the following system of equations:
11.5X + 4.5Y = 10,000 ---(1)
1.5X - 0.5Y = 275 ---(2)
Solving these equations, we get:
X = 510
Therefore, the cost price of a shirt is Rs. 510.
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The cost price of 10 shirts and 5 trousers together is Rs. 10,000, A shopkeeper sells shirts at a profit of 15% and trousers at a loss of 10% and his overall gain is Rs. 275. Find the cost price of a shirt.Correct answer is '510'. Can you explain this answer?
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The cost price of 10 shirts and 5 trousers together is Rs. 10,000, A shopkeeper sells shirts at a profit of 15% and trousers at a loss of 10% and his overall gain is Rs. 275. Find the cost price of a shirt.Correct answer is '510'. 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 The cost price of 10 shirts and 5 trousers together is Rs. 10,000, A shopkeeper sells shirts at a profit of 15% and trousers at a loss of 10% and his overall gain is Rs. 275. Find the cost price of a shirt.Correct answer is '510'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The cost price of 10 shirts and 5 trousers together is Rs. 10,000, A shopkeeper sells shirts at a profit of 15% and trousers at a loss of 10% and his overall gain is Rs. 275. Find the cost price of a shirt.Correct answer is '510'. Can you explain this answer?.
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