Question

Price of a commodity decreased by 10% last year and increased by 20% this year. Find the % change in two years.

Answer 1

Let the price of the commodity before last year = x

the last year price is decreased by 10%.

Therefore price of commodity in the last year = x - 10% of x = $x-\frac{10x}{100}$ = $\frac{100x-10x}{100}$ = $\frac{9x}{10}$.

Now in the current year commodity is increased by 20%.

Therefore price of commodity this year = $\frac{9x}{10}$ + 20% of $\frac{9x}{10}$ = $\frac{9x}{10}$ + $\frac{20}{100}$ $\times$$\frac{9x}{10}$ = $\frac{9x}{10}$ (1 + $\frac{1}{5}$) = $\frac{9x}{10}$ ($\frac{6}{5}$) = $\frac{54x}{50}$.

So, % change in two years = $\frac{pricethisyear-originalprice}{originalprice}$ $\times$ 100 = $\frac{\frac{54x}{50}-x}{x}$ $\times$ 100 = $\frac{54x-50x}{50x}$ $\times$ 100 = $\frac{4x}{50x}\times 100$ = 8%.

Hence, % change in 2 years is 8%.