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Shopkeepers A and B mark a particular item at the same price. A gives three successive discounts of x%, y% and z% on the item. B gives a single discount of (x + y + z)% on the item. Then, which of the following is true?
- a)A and B both make a profit.
- b)A makes a profit and B makes a loss.
- c)Selling price of A is higher than that of B.
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Shopkeepers A and B mark a particular item at the same price. A gives ...
Given:
Shopkeepers A and B mark a particular item at the same price.
A gives three successive discounts of x%, y%, and z% on the item.
B gives a single discount of (x - y - z)% on the item.
To determine whether the selling price of A is higher than that of B, we need to compare their selling prices.
Let's assume the marked price of the item is M.
Shopkeeper A's selling price:
After the first discount of x%, the selling price becomes M - (x/100) * M = M(1 - x/100).
After the second discount of y%, the selling price becomes M(1 - x/100)(1 - y/100).
After the third discount of z%, the selling price becomes M(1 - x/100)(1 - y/100)(1 - z/100).
Shopkeeper B's selling price:
After the single discount of (x - y - z)%, the selling price becomes M - ((x - y - z)/100) * M = M(1 - (x - y - z)/100).
Now, we need to compare the two selling prices:
M(1 - x/100)(1 - y/100)(1 - z/100) vs M(1 - (x - y - z)/100)
We can simplify this by expanding the expressions:
M(1 - x/100)(1 - y/100)(1 - z/100) = M(1 - (x + y + z - xy/100 - yz/100 - xz/100 + xyz/10000))
M(1 - (x - y - z)/100) = M - M(x - y - z)/100
Comparing the two selling prices, we can observe that M(1 - x/100)(1 - y/100)(1 - z/100) is greater than M - M(x - y - z)/100.
Therefore, the selling price of A is higher than that of B. Hence, option C is correct.
Shopkeepers A and B mark a particular item at the same price.
A gives three successive discounts of x%, y%, and z% on the item.
B gives a single discount of (x - y - z)% on the item.
To determine whether the selling price of A is higher than that of B, we need to compare their selling prices.
Let's assume the marked price of the item is M.
Shopkeeper A's selling price:
After the first discount of x%, the selling price becomes M - (x/100) * M = M(1 - x/100).
After the second discount of y%, the selling price becomes M(1 - x/100)(1 - y/100).
After the third discount of z%, the selling price becomes M(1 - x/100)(1 - y/100)(1 - z/100).
Shopkeeper B's selling price:
After the single discount of (x - y - z)%, the selling price becomes M - ((x - y - z)/100) * M = M(1 - (x - y - z)/100).
Now, we need to compare the two selling prices:
M(1 - x/100)(1 - y/100)(1 - z/100) vs M(1 - (x - y - z)/100)
We can simplify this by expanding the expressions:
M(1 - x/100)(1 - y/100)(1 - z/100) = M(1 - (x + y + z - xy/100 - yz/100 - xz/100 + xyz/10000))
M(1 - (x - y - z)/100) = M - M(x - y - z)/100
Comparing the two selling prices, we can observe that M(1 - x/100)(1 - y/100)(1 - z/100) is greater than M - M(x - y - z)/100.
Therefore, the selling price of A is higher than that of B. Hence, option C is correct.
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Community Answer
Shopkeepers A and B mark a particular item at the same price. A gives ...
As no data about the cost price of that particular item is given, we cannot determine whether they made a profit or loss. Thus, [1] and [2] are false.
Now, the discount given by B = (x + y + z)%, whereas discount given by A
Thus, the discount given by A is lesser than that of B.
So, the selling price of A is higher than that of B.
Now, the discount given by B = (x + y + z)%, whereas discount given by A
Thus, the discount given by A is lesser than that of B.
So, the selling price of A is higher than that of B.
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Shopkeepers A and B mark a particular item at the same price. A gives three successive discounts of x%, y% and z% on the item. B gives a single discount of (x + y + z)% on the item. Then, which of the following is true?a)A and B both make a profit.b)A makes a profit and B makes a loss.c)Selling price of A is higher than that of B.d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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Shopkeepers A and B mark a particular item at the same price. A gives three successive discounts of x%, y% and z% on the item. B gives a single discount of (x + y + z)% on the item. Then, which of the following is true?a)A and B both make a profit.b)A makes a profit and B makes a loss.c)Selling price of A is higher than that of B.d)None of theseCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Shopkeepers A and B mark a particular item at the same price. A gives three successive discounts of x%, y% and z% on the item. B gives a single discount of (x + y + z)% on the item. Then, which of the following is true?a)A and B both make a profit.b)A makes a profit and B makes a loss.c)Selling price of A is higher than that of B.d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Shopkeepers A and B mark a particular item at the same price. A gives three successive discounts of x%, y% and z% on the item. B gives a single discount of (x + y + z)% on the item. Then, which of the following is true?a)A and B both make a profit.b)A makes a profit and B makes a loss.c)Selling price of A is higher than that of B.d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
Shopkeepers A and B mark a particular item at the same price. A gives three successive discounts of x%, y% and z% on the item. B gives a single discount of (x + y + z)% on the item. Then, which of the following is true?a)A and B both make a profit.b)A makes a profit and B makes a loss.c)Selling price of A is higher than that of B.d)None of theseCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Shopkeepers A and B mark a particular item at the same price. A gives three successive discounts of x%, y% and z% on the item. B gives a single discount of (x + y + z)% on the item. Then, which of the following is true?a)A and B both make a profit.b)A makes a profit and B makes a loss.c)Selling price of A is higher than that of B.d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Shopkeepers A and B mark a particular item at the same price. A gives three successive discounts of x%, y% and z% on the item. B gives a single discount of (x + y + z)% on the item. Then, which of the following is true?a)A and B both make a profit.b)A makes a profit and B makes a loss.c)Selling price of A is higher than that of B.d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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