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A shopkeeper sells a commodity with a profit of 30 percent on the cost
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13 Oct 2023, 08:10
13 Oct 2023, 08:10
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Question Stats:
60% (01:58) correct
40% (01:32) wrong based on 5 sessions
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A shopkeeper sells a commodity with a profit of 30 percent on the cost of the commodity. If the selling price were increased by $100, it would yield a profit of 40 percent of the commodity’s cost. What was the initial selling price of the commodity?
(A) $1,000
(B) $1,200
(C) $1,300
(D) $1,400
(E) $1,800
(A) $1,000
(B) $1,200
(C) $1,300
(D) $1,400
(E) $1,800
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Re: A shopkeeper sells a commodity with a profit of 30 percent on the cost
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13 Jan 2024, 06:26
13 Jan 2024, 06:26
Expert Reply
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A shopkeeper sells a commodity with a profit of 30 percent on the cost
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18 Jan 2024, 14:49
18 Jan 2024, 14:49
1
The profit percentage formula is (selling price - cost)/cost * 100 = profit percentage
Let \(s\) = initial selling price, \(c\) = commodity's cost.
Since we're given the initial profit percentage is 30%,
\(\frac{s - c}{c} * 100 = 30\)
\(s - c = 0.3c\)
\(s = 1.3c\)
The new selling price after the increase = s + 100. Set up the formula again with the new profit percentage of 40%.
\(\frac{(s + 100)- c}{c} * 100 = 40\) <- c remains the same, since cost doesn't change
\((s + 100)- c = 0.4c\)
\(s + 100 = 1.4c\)
Plug in \(s = 1.3c\) for s to solve for c.
\(1.3c + 100 = 1.4c\)
\(100 = 0.1c\)
\(c = 1000\)
\(s = 1.3c = 1.3(1000) = 1300\)
Let \(s\) = initial selling price, \(c\) = commodity's cost.
Since we're given the initial profit percentage is 30%,
\(\frac{s - c}{c} * 100 = 30\)
\(s - c = 0.3c\)
\(s = 1.3c\)
The new selling price after the increase = s + 100. Set up the formula again with the new profit percentage of 40%.
\(\frac{(s + 100)- c}{c} * 100 = 40\) <- c remains the same, since cost doesn't change
\((s + 100)- c = 0.4c\)
\(s + 100 = 1.4c\)
Plug in \(s = 1.3c\) for s to solve for c.
\(1.3c + 100 = 1.4c\)
\(100 = 0.1c\)
\(c = 1000\)
\(s = 1.3c = 1.3(1000) = 1300\)
