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A shopkeeper sold 10 items, all of which are of the same cost price, such that profit percentage on no two item is the same. The profits made on the given items were in an arithmetic progression. If the profit percentage of the item the selling price of which is 4th highest and the item the selling price of which is 7th highest were 13 % and 10 % respectively, find the profit percentage on the whole.
(2015)
- a)11.5%
- b)12%
- c)12.5%
- d)Data insufficient
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A shopkeeper sold 10 items, all of which are of the same cost price, s...
If the profit amount are in AP then the profit % ages are also in an A.P.
If P4 = 13%
and P7 = 10%
then P5 = 12%
and P6 = 11%
Average of the middle terms will give the profit % on the whole i.e. (11 +12)/2 = 11.5 %
If P4 = 13%
and P7 = 10%
then P5 = 12%
and P6 = 11%
Average of the middle terms will give the profit % on the whole i.e. (11 +12)/2 = 11.5 %
Most Upvoted Answer
A shopkeeper sold 10 items, all of which are of the same cost price, s...
Given:
- The shopkeeper sold 10 items at the same cost price.
- The profit percentage on no two items is the same.
- The profits made on the items were in an arithmetic progression.
- The profit percentage of the item with the 4th highest selling price is 13%.
- The profit percentage of the item with the 7th highest selling price is 10%.
To find: The profit percentage on the whole.
Approach:
Let the cost price of each item be x.
Let the profits made on the items be a, a+d, a+2d,..., a+9d.
Let the selling prices of the items be x(1+a/100), x(1+(a+d)/100),..., x(1+(a+9d)/100).
Given that the profit percentages on no two items are the same, we can assume that the common difference (d) is not equal to 0.
We know that the profit percentage of the item with the 4th highest selling price is 13%.
Therefore, x(1+(a+3d)/100) = x(1.13).
Simplifying this equation, we get a+3d = 13x/100.
We also know that the profit percentage of the item with the 7th highest selling price is 10%.
Therefore, x(1+(a+6d)/100) = x(1.1).
Simplifying this equation, we get a+6d = 10x/100.
We can solve these two equations to get x in terms of d.
On substituting this value of x in the expression for the selling price of any item, we get the profit percentage on the whole.
Calculation:
a+3d = 13x/100
a+6d = 10x/100
On solving these two equations, we get:
x = 60d/17
a = 9d/17
Substituting these values in the expression for the selling price of any item, we get:
Selling price = x(1+nd/100) = (60d/17)(1+nd/100)
The profits made on the items are in arithmetic progression. Therefore, the common difference (d) can be written as a multiple of the first term (a).
Let the common ratio be r. Then, d = ar.
Substituting this value of d in the expression for the selling price, we get:
Selling price = (60a/17)(1+nr)
We know that the profit percentage of the item with the 4th highest selling price is 13%.
Therefore, (60a/17)(1+3r) = (113/100)(60a/17).
Solving this equation, we get r = 1/17.
Substituting this value of r in the expression for the selling price, we get:
Selling price = (60a/17)(1+n/17)
We also know that the profit percentage of the item with the 7th highest selling price is 10%.
Therefore, (60a/17)(1+6r) = (110/100)(60a/17).
Solving this equation, we get n = 6.
Substituting these values of a, n, and r in the expression for the selling price
- The shopkeeper sold 10 items at the same cost price.
- The profit percentage on no two items is the same.
- The profits made on the items were in an arithmetic progression.
- The profit percentage of the item with the 4th highest selling price is 13%.
- The profit percentage of the item with the 7th highest selling price is 10%.
To find: The profit percentage on the whole.
Approach:
Let the cost price of each item be x.
Let the profits made on the items be a, a+d, a+2d,..., a+9d.
Let the selling prices of the items be x(1+a/100), x(1+(a+d)/100),..., x(1+(a+9d)/100).
Given that the profit percentages on no two items are the same, we can assume that the common difference (d) is not equal to 0.
We know that the profit percentage of the item with the 4th highest selling price is 13%.
Therefore, x(1+(a+3d)/100) = x(1.13).
Simplifying this equation, we get a+3d = 13x/100.
We also know that the profit percentage of the item with the 7th highest selling price is 10%.
Therefore, x(1+(a+6d)/100) = x(1.1).
Simplifying this equation, we get a+6d = 10x/100.
We can solve these two equations to get x in terms of d.
On substituting this value of x in the expression for the selling price of any item, we get the profit percentage on the whole.
Calculation:
a+3d = 13x/100
a+6d = 10x/100
On solving these two equations, we get:
x = 60d/17
a = 9d/17
Substituting these values in the expression for the selling price of any item, we get:
Selling price = x(1+nd/100) = (60d/17)(1+nd/100)
The profits made on the items are in arithmetic progression. Therefore, the common difference (d) can be written as a multiple of the first term (a).
Let the common ratio be r. Then, d = ar.
Substituting this value of d in the expression for the selling price, we get:
Selling price = (60a/17)(1+nr)
We know that the profit percentage of the item with the 4th highest selling price is 13%.
Therefore, (60a/17)(1+3r) = (113/100)(60a/17).
Solving this equation, we get r = 1/17.
Substituting this value of r in the expression for the selling price, we get:
Selling price = (60a/17)(1+n/17)
We also know that the profit percentage of the item with the 7th highest selling price is 10%.
Therefore, (60a/17)(1+6r) = (110/100)(60a/17).
Solving this equation, we get n = 6.
Substituting these values of a, n, and r in the expression for the selling price
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Community Answer
A shopkeeper sold 10 items, all of which are of the same cost price, s...
If the profit amount are in AP then the profit % ages are also in an A.P.
If P4 = 13%
and P7 = 10%
then P5 = 12%
and P6 = 11%
Average of the middle terms will give the profit % on the whole i.e. (11 +12)/2 = 11.5 %
If P4 = 13%
and P7 = 10%
then P5 = 12%
and P6 = 11%
Average of the middle terms will give the profit % on the whole i.e. (11 +12)/2 = 11.5 %
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A shopkeeper sold 10 items, all of which are of the same cost price, such that profit percentage on no two item is the same. The profits made on the given items were in an arithmetic progression. If the profit percentage of the item the selling price of which is 4th highest and the item the selling price of which is 7th highest were 13 % and 10 % respectively, find the profit percentage on the whole.(2015)a)11.5%b)12%c)12.5%d)Data insufficientCorrect answer is option 'A'. Can you explain this answer?
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A shopkeeper sold 10 items, all of which are of the same cost price, such that profit percentage on no two item is the same. The profits made on the given items were in an arithmetic progression. If the profit percentage of the item the selling price of which is 4th highest and the item the selling price of which is 7th highest were 13 % and 10 % respectively, find the profit percentage on the whole.(2015)a)11.5%b)12%c)12.5%d)Data insufficientCorrect answer is option 'A'. 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 A shopkeeper sold 10 items, all of which are of the same cost price, such that profit percentage on no two item is the same. The profits made on the given items were in an arithmetic progression. If the profit percentage of the item the selling price of which is 4th highest and the item the selling price of which is 7th highest were 13 % and 10 % respectively, find the profit percentage on the whole.(2015)a)11.5%b)12%c)12.5%d)Data insufficientCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shopkeeper sold 10 items, all of which are of the same cost price, such that profit percentage on no two item is the same. The profits made on the given items were in an arithmetic progression. If the profit percentage of the item the selling price of which is 4th highest and the item the selling price of which is 7th highest were 13 % and 10 % respectively, find the profit percentage on the whole.(2015)a)11.5%b)12%c)12.5%d)Data insufficientCorrect answer is option 'A'. Can you explain this answer?.
A shopkeeper sold 10 items, all of which are of the same cost price, such that profit percentage on no two item is the same. The profits made on the given items were in an arithmetic progression. If the profit percentage of the item the selling price of which is 4th highest and the item the selling price of which is 7th highest were 13 % and 10 % respectively, find the profit percentage on the whole.(2015)a)11.5%b)12%c)12.5%d)Data insufficientCorrect answer is option 'A'. 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 A shopkeeper sold 10 items, all of which are of the same cost price, such that profit percentage on no two item is the same. The profits made on the given items were in an arithmetic progression. If the profit percentage of the item the selling price of which is 4th highest and the item the selling price of which is 7th highest were 13 % and 10 % respectively, find the profit percentage on the whole.(2015)a)11.5%b)12%c)12.5%d)Data insufficientCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shopkeeper sold 10 items, all of which are of the same cost price, such that profit percentage on no two item is the same. The profits made on the given items were in an arithmetic progression. If the profit percentage of the item the selling price of which is 4th highest and the item the selling price of which is 7th highest were 13 % and 10 % respectively, find the profit percentage on the whole.(2015)a)11.5%b)12%c)12.5%d)Data insufficientCorrect answer is option 'A'. Can you explain this answer?.
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A shopkeeper sold 10 items, all of which are of the same cost price, such that profit percentage on no two item is the same. The profits made on the given items were in an arithmetic progression. If the profit percentage of the item the selling price of which is 4th highest and the item the selling price of which is 7th highest were 13 % and 10 % respectively, find the profit percentage on the whole.(2015)a)11.5%b)12%c)12.5%d)Data insufficientCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A shopkeeper sold 10 items, all of which are of the same cost price, such that profit percentage on no two item is the same. The profits made on the given items were in an arithmetic progression. If the profit percentage of the item the selling price of which is 4th highest and the item the selling price of which is 7th highest were 13 % and 10 % respectively, find the profit percentage on the whole.(2015)a)11.5%b)12%c)12.5%d)Data insufficientCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A shopkeeper sold 10 items, all of which are of the same cost price, such that profit percentage on no two item is the same. The profits made on the given items were in an arithmetic progression. If the profit percentage of the item the selling price of which is 4th highest and the item the selling price of which is 7th highest were 13 % and 10 % respectively, find the profit percentage on the whole.(2015)a)11.5%b)12%c)12.5%d)Data insufficientCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A shopkeeper sold 10 items, all of which are of the same cost price, such that profit percentage on no two item is the same. The profits made on the given items were in an arithmetic progression. If the profit percentage of the item the selling price of which is 4th highest and the item the selling price of which is 7th highest were 13 % and 10 % respectively, find the profit percentage on the whole.(2015)a)11.5%b)12%c)12.5%d)Data insufficientCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
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