Problem Solving

Mikrislac wrote: ↑

Tue Aug 18, 2020 11:11 pm

After selling a watch, Watch store found that it had incurred a loss of 10%. If Watch store had instead sold the watch for $27 more, then it would have made a profit of 5%. If Watch store had sold the watch for a 5% profit, what would have been the actual initial loss as a percentage of the profit earned?

(A) 120%

(B) 150%

(C) 180%

(D) 200%

(E) 250%

Solution:

We can let the cost of the watch be x dollars and the initial price of the watch be y dollars. Since the watch is sold at the initial price and it has incurred a loss of 10%, the initial loss, as a dollar amount, is x - y. Had the watch been sold for $27 more, it would have made a profit of 5%. Therefore, the profit, as a dollar amount, is y + 27 - x. We need to compute the value of
(x - y)/(y + 27 - x) * 100. Therefore, we need to solve for x and y first. We can create the equations:

y = 0.9x

and

y + 27 = 1.05x

Subtracting the first equation from the second, we have:

27 = 0.15x

x = 27/0.15 = 2700/15 = 180

Therefore, y = 0.9(180) = 162. So the initial loss is 180 - 162 = $18 and the would-be profit earned is 162 + 27 - 180 = $9. Therefore, the percentage is 18/9 * 100 = 200 percent.

Answer: D