Question

The original price of a shirt was \[\$ 20\] . It was decreased to \[\$ 15\] . What is the percent decrease of the price of this shirt?

Answer 1

Hint: First find the absolute decreased amount and then divide it by the original price of the shirt to get the percent change. After that multiply and divide the obtained result to get the answer in percentage.

Complete step-by-step answer:
It is given in the problem that the original price of a shirt was \[\$ 20\] and it was decreased to \[\$ 15\] .
We have to find the percent decrease of the price of this shirt.
Original price of the shirt \[ = \$ 20\]
New price of the shirt \[ = \$ 15\]
First, we find the absolute decrease in the price of the shirt by taking the difference of the original price with the new price.
Absolute change in price \[ = \$ 20 - \$ 15 = \$ 5\]
Now, we know that there is a change of \[\$ 5\] in the price of the shirt.
Now, we get the percent decrease by dividing the absolute change in the price with the original price of the shirt.
Percent decrease \[ = \dfrac{5}{{20}}\]
Percent decrease \[ = 0.25\]
Now, we convert it into the percent by dividing and multiplying it by\[100\].
Percent decrease \[ = \dfrac{{0.25}}{{100}} \times 100\]
Percent decrease \[ = 25\% \]
Therefore, we get that there is a \[25\% \] decrease in the price of the shirt.

Note: There is an alternate method to find the percent decrease in the price of shirt, directly using the formula.
Original price of the shirt \[ = \$ 20\]
New price of the shirt \[ = \$ 15\]
Usual formula for finding the decrease percent is given as:
Decrease percent \[ = \dfrac{{{\rm{Original\, price}} - {\rm{New price}}}}{{{\rm{Original\, Price}}}} \times 100\]
Substitute original price as \[20\], new price as\[15\] in the above formula:
Decrease percent \[ = \left( {\dfrac{{20 - 15}}{{20}} \times 100} \right)\% \]
Evaluate the decrease percent:
Decrease percent \[ = \left( {\dfrac{5}{{20}} \times 100} \right)\% \]
Decrease percent \[ = \left( {5 \times 5} \right)\% \]
Decrease percent \[ = 25\% \]
Hence, we get that there is a \[25\% \] decrease in the price of the shirt.