Arithmetic price and revenue problem.

Question

In 2005, the number of pairs of shoes that a company sold to retailers decreased by 20%, while the price per pair increased by 20% from that of the previous year. The revenue from the sales of shoes in 2005 was Rs. 300,000. What was the revenue from the sales of shoes the previous year?

Answer 1

Let's make P = the price of the shoe in 2004 and N = the number of shoes sold in 2004

in 2005, we have 120% of the Price and 80% of the number of shoes sold, which multiply together to equal the total revenue. Converting our percentages into decimals, this means we can write an equation of (1.2*P)*(0.8*N) = 300,000. Multiplying our left side gets us 0.96*PN = 300,000. PN is the Price and Number sold in 2004, so isolating them will grant us the answer. Simply divide both sides by 0.96 and you will get PN = 312,500.

Answer 2

Suppose N pairs of shoes were sold in 2004, at price P

Then in 2005, 0.8 N pairs were sold at a price of 1.2 P

So revenue in 2005 is 0.8 N X 1.2 P = 300000, giving NP = 300000 / (1.2 X 0.8) = 312500 Rs

This was the revenue in 2004 (revenue = price x number sold)