pushpitkc wrote:
A merchant made a gross profit of $40 from the sale of a vase. If this gross profit was 25 percent of the cost of the vase to the merchant, for how many dollars more should the merchant have sold the vase for the gross profit to have been 30 percent of the cost?
(A) $2
(B) $5
(C) $8
(D) $10
(E) $12
If the profit increases by $x, then the selling price also increases by $x.
Implication:
To determine the required increase in the selling price, we need to determine only the required increase in the profit.
Old profit percentage = 25
New profit percentage = 30
Percent change from 25 to 30:
\(\frac{Difference}{Original} * 100 = \frac{30-25}{25} * 100 = 20\)
For the profit percentage to increase by 20%, the profit in dollars must also increase by 20%:
20% of original profit \(= \frac{20}{100} * 40 = 8\)
Another example with different values:
Quote:
A merchant made a gross profit of $20 from the sale of a vase. If this gross profit was 10 percent of the cost of the vase to the merchant, for how many dollars more should the merchant have sold the vase for the gross profit to have been 50 percent of the cost?
Old profit percentage = 10
New profit percentage = 50
Percent change from 10 to 50:
\(\frac{Difference}{Original} * 100 = \frac{50-10}{10} * 100 = 400\)
For the profit percentage to increase by 400%, the profit in dollars must also increase by 400%:
400% of original profit \(= \frac{400}{100} * 20 = 80\)
In this case:
Merchant cost = 200
Original profit = 20
Original profit percentage = \(\frac{20}{200} =\) 10%
New profit = 20+80 = 100
New profit percentage = \(\frac{100}{200} =\) 50%