A merchant made a gross profit of $40 from the sale of a vase. If this

Cost of the vase: \(\frac{40}{.25} = \frac{40}{\frac{1}{4}}\) = 40*4 = 160

We want to find out how much 30%-25% = 5% of the cost is; 10% of 160 is 16, therefore 5% of 160 = 16/2 = 8

Bunuel
Hello Experts,
I think all the answers given for this question are wrong.
I mean, 160 + 8 = 168.
30% of 168 = 50.4.
So 8 can't possibly be the correct answer for this question.
Since 25% is 40, so the Original price is 160. Now, if we wanted 30% profit from it, we don't actually need to increase or decrease anything.
If we wanted 40 to represent 30% of the price then we would have to reduce the price to 133.33 and not increase it.
So the question and the answer choices make no sense in my opinion. Also, all the answers make no sense to me.
If I am wrong, can anyone please help me understand where I am going wrong?
Thanks for any help.

Yes, you are wrong and "all these people" are right.

Since $40 represents 25% of the cost of the vase to the merchant, then the cost of the vase to the merchant is $160. The price at which the vase is sold is therefore, $200.

30% of the cost is 0.3*160 = $48. So, the merchant should have sold the vase for $208, hence by $8 more, for the gross profit ($48) to have been 30% of the cost ($160).

The vase has to be sold for 160+40+8, as we are looking for how much more should he have sold it for. He was already selling it for 160+40 or 200.
30% of 160 is 48 or it should have been sold for 160+48, which is same as 160+40+8.

Oops, silly me. Too much coffee I guess, not thinking straight.
Well, I have solved almost all the official questions of this type and all the others and didn't see a question like this, until now. I just assumed the profit to have been counted in, didn't pay enough attention to the word "Cost".
Good lesson, Thanks

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:



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%