Question

Price of commodities decreased by \[10\% \] last year and increased by \[20\% \] this year. Find the percentage change in two years.

Answer 1

Hint: We are provided that the price of a commodity fell by \[10\% \] last year and this year it has increased by \[20\% \] . We have to find a percentage change in two years. To solve this question, we need to find the price of commodities last year as well this year too and then we will use the percentage change formula to calculate the overall percentage change.

FORMULA TO BE USED:
Percentage change in $2$ years $ = $ This year price-original price $/$ original price \[ \times 100\]

Complete step-by-step answer:
Let the price of the commodity before the last year be \[x\] rupees
Last year the price decreased by $10\% $ [According to question].
Then, the price of the commodity in last year will be $ = x - 10\% $ of \[x\]
$ \Rightarrow x - \dfrac{{10x}}{{100}}$
\[\dfrac{{100x - 10x}}{{100}} = \dfrac{{9x}}{{10}}\]
Therefore, the price of the commodity last year was \[\dfrac{{9x}}{{10}}\].
Now this year the price of the commodity has increased by $20\% $ [according to question].
The price of the commodity this year $ = \dfrac{{9x}}{{10}} + 20\% $ of $\dfrac{{9x}}{{10}}$
=\[\dfrac{{9x}}{{10}} + \dfrac{{20}}{{100}} \times \dfrac{{9x}}{{10}}\]
\[\dfrac{{9x}}{{10}} + \dfrac{1}{5} \times \dfrac{{9x}}{{10}} = \dfrac{{9x}}{{10}} + \dfrac{{9x}}{{50}}\]
\[ = \dfrac{{45x + 9x}}{{50}}\]
\[ = \dfrac{{54x}}{{50}}\]
So, percentage change in two years $ = $ This year price-original price $/$ original price \[ \times 100\]
\[\dfrac{{\dfrac{{54x}}{{50}} - x}}{x} \times 100 = \dfrac{{\dfrac{{54x - 50x}}{{50}}}}{x}\] [ Original price $ = $ \[x\]rupees, this year price =\[\dfrac{{54x}}{{50}}\]]
\[\dfrac{{4x}}{{50x}} \times 100 = 8\% \]
Hence percentage change in two year is \[8\% \]

Note: ALTERNATIVE METHOD
Let the price of a commodity be \[x\] rupees.
Price of a commodity Fall by $10\% $ last year [according to question]
So, price of commodity Last year is \[ = 100 - \dfrac{{10}}{{100}} \times 100\]
$ = 90$ Rupees
Price of commodity increased by $20\% $ this year [according to question]
Price of commodity in this year is \[ = 90 + \dfrac{{20}}{{100}} \times 90\]
$ = 108$ Rupees
The percentage change in two years \[ = \dfrac{8}{{100}} \times 100\]
\[ = 8\% \]
Therefore, the percentage change in two years is \[8\% \] .
We can apply any method provided above to solve the question.