Problem Solving

Source: Princeton Review

Between the first day of May and the last day in June, the price per kilogram of Melange, a seasoning mix, first declined by 20 percent and then increased by 50 percent. During this same period, the price per liter of Blue, a spring water, first increased by 20 percent and then declined by 50 percent. If at the end of June, the prices were the same, then, at the beginning of May, the price per kilogram for Blue was what percent of the price per liter of Melange?

A. 2
B. 30
C. 50
D. 100
E. 200

The OA is E

BTGmoderatorLU wrote:Source: Princeton Review

Between the first day of May and the last day in June, the price per kilogram of Melange, a seasoning mix, first declined by 20 percent and then increased by 50 percent. During this same period, the price per liter of Blue, a spring water, first increased by 20 percent and then declined by 50 percent. If at the end of June, the prices were the same, then, at the beginning of May, the price per kilogram for Blue was what percent of the price per liter of Melange?

A. 2
B. 30
C. 50
D. 100
E. 200

We can PLUG IN THE ANSWERS.
When the correct answer is plugged in, Blue's resulting price and Melange's resulting price will be EQUAL.

D: 100
Here, Blue's initial price is 100% of Melange's initial price, implying that the two initial prices are equal.
Let Blue = May = $100.
From May to June:
Blue's $100 initial price increases by 20% to $120 and then decreases by 50% to $60.
Melange's $100 initial price increases by 50% to $150 and then decreases by 20% to $120.
In this case, Blue's resulting price is LESS THAN Melange's resulting price.
Implication:
For the two resulting prices to be equal, Blue's initial price must be a higher percentage of Melange's initial price.

The correct answer is E.

Algebra:

Blue increased by 20 percent and then declined by 50 percent.
B * 120/100 * 50/100 = B * 6/5 * 1/2 = (3/5)B.
Melange declined by 20 percent and then increased by 50 percent.
M * 80/100 * 150/100 = M * 4/5 * 3/2 = (6/5)M.
Since the two resulting prices are equal, we get:
(3/5)B = (6/5)M
3B = 6M
B = 2M
Since B is twice the value of M, Blue's initial price is equal to 200% of Melange's initial price.