Problem Solving

In 1985 a company sold a brand of shoes to retailers for a fixed price per pair. In 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent, while the price per pair increased by 20 percent. If the company's revenue from the sale of the shoes in 1986 was $3.0 million, what was the approximate revenue from the sale of the shoes in 1985?

(A) $2.4 million
(B) $2.9 million
(C) $3.0 million
(D) $3.1 million
(E) $3.6 million

[quote="Architj"]In 1985 a company sold a brand of shoes to retailers for a fixed price per pair. In 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent, while the price per pair increased by 20 percent. If the company's revenue from the sale of the shoes in 1986 was $3.0 million, what was the approximate revenue from the sale of the shoes in 1985?

(A) $2.4 million
(B) $2.9 million
(C) $3.0 million
(D) $3.1 million
(E) $3.6 million[/quote]

Suppose in the year 1985 the number of pairs of shoes sold = 100 &
the price per pair = 100 => the Total Revenue = 100x100 = 10000

Then in the year 1986 the number of pairs of shoes sold = 80 &
the price per pair = 120 => the Total Revenue = 80x120 = 9600

It is given the company's revenue from the sale of the shoes in 1986 was $3.0 million
So if 9600 equals $3.0 million
then 10000 equals = (10000/9600)x $3.0 million = 1.042 x $3.0 million = 3.125 million

Answer [spoiler]D[/spoiler]

Architj wrote:In 1985 a company sold a brand of shoes to retailers for a fixed price per pair. In 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent, while the price per pair increased by 20 percent. If the company's revenue from the sale of the shoes in 1986 was $3.0 million, what was the approximate revenue from the sale of the shoes in 1985?

(A) $2.4 million
(B) $2.9 million
(C) $3.0 million
(D) $3.1 million
(E) $3.6 million

To determine the revenue ratio for 1986 to 1985, TEST AN EASY CASE.

1985:
Let the number of pairs sold = 10.
Let the price per pair = 10.
Total revenue = (number of pairs)(price per pair) = 10*10 = 100.

1986:
Since 20% fewer pairs are sold, the number of pairs = 10 - 20% of 10 = 10-2 = 8.
Since the price per pair increases by 20%, the price per pair = 10 + 20% of 10 = 10+2 = 12.
Total revenue = (number of pairs)(price per pair) = 8*12 = 96.

Resulting ratio:
(revenue in 1986)/(revenue in 1985) = 96/100 = 24/25.

Since the actual revenue in 1986 = 3 million, set up the following proportion:
24/25 = 3/x
24x = 75
x = 3.125.

The correct answer is D.

Hi ,

Can you please advise that why did you do by taking ratio? Is there any other method to solve this?

Resulting ratio:
(revenue in 1986)/(revenue in 1985) = 96/100 = 24/25.

Since the actual revenue in 1986 = 3 million, set up the following proportion:
24/25 = 3/x
24x = 75
x = 3.125.