The unitary method and reverse percentages

Using the unitary method to find the original amount before a percentage change, and other percentage problems.

Find one unit first

Example 1●

$15\%$ of a number is $45$. Find the number.

$1\% = 45 \div 15 = 3$

$100\% = 300$

Example 2●●

After a $20\%$ discount, a jacket costs $\$96$. What was the original price?

$80\% = 96$

The sale price is 100% − 20% = 80% of the original.

$1\% = 1.2$, so $100\% = \$120$.

Example 3●●

A price including $10\%$ GST is $\$341$. Find the price before GST.

$110\% = 341$, so $1\% = 3.1$.

$100\% = \$310$.

Flashcards

Unitary method

Find 1%, then scale up.

After 25% off, price is...

75% of the original.

Price including GST

110% of the price before GST.

Practice

$15\%$ of a number is $45$. Find the number.
After a $20\%$ discount a jacket costs $\$96$. Find the original price.
Including $10\%$ GST a price is $\$341$. Find the price before GST.
$40\%$ of a number is $320$. Find the number.
After a $25\%$ pay rise, a wage is $\$75$ per hour. Find the original hourly wage.
A shop sells $30\%$ of its stock, which is $75$ items. How many items did it start with?
After a $10\%$ decrease, a value is $45$. Find the original value.
After $25\%$ off, a price is $\$60$. The original price is: