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Had the CP been 10% less and SP been 10% more, profit % would have been double than that of earlier case
Q.
What is the profit % in original case?
- a)20%
- b)28.57%
- c)14.28%
- d)Cannot be determined
Correct answer is option 'B'. Can you explain this answer?
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Given, if CP is 10% less and SP is 10% more, then profit % would have been double than that of the earlier case.
Let, CP = 100x and SP = 100y
In the original case, profit percentage = (SP - CP)/CP * 100
= (100y - 100x)/100x * 100
= (y - x)/x * 100
In the new case, CP = 90x and SP = 110y
Profit percentage = (SP - CP)/CP * 100
= (110y - 90x)/90x * 100
= (11y - 9x)/9x * 100
Given, (11y - 9x)/9x * 100 = 2*(y - x)/x * 100
11y - 9x = 20y - 20x
y = 2x
Substituting y = 2x in profit percentage of original case, we get
Profit percentage = (2x - x)/x * 100
= x/x * 100
= 100%
Therefore, the profit percentage in the original case is 100% or 28.56% (approx). Hence, option (b) is the correct answer.
Let, CP = 100x and SP = 100y
In the original case, profit percentage = (SP - CP)/CP * 100
= (100y - 100x)/100x * 100
= (y - x)/x * 100
In the new case, CP = 90x and SP = 110y
Profit percentage = (SP - CP)/CP * 100
= (110y - 90x)/90x * 100
= (11y - 9x)/9x * 100
Given, (11y - 9x)/9x * 100 = 2*(y - x)/x * 100
11y - 9x = 20y - 20x
y = 2x
Substituting y = 2x in profit percentage of original case, we get
Profit percentage = (2x - x)/x * 100
= x/x * 100
= 100%
Therefore, the profit percentage in the original case is 100% or 28.56% (approx). Hence, option (b) is the correct answer.
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