# Finding the original amount given the result of a percentage increase or decrease

In this lesson, we learn how to find the original amount, given result of a percent increase or decrease.

**Rules to find the original amount given the result of a percentage increase or decrease**

First consider the unknown original amount as ‘

*x*’.Then consider the percent rate of increase or decrease

To find the increase or decrease, multiply the rate by the original amount ‘

*x*’.To find the final amount, add or subtract the increase or decrease to the original amount ‘

*x*’ and equate this to given final amount.Solve the equation and find the original amount ‘

*x*’.

After a 25% increase, a TV was $750. Find the original price

### Solution

**Step 1:**

Let the original amount be = *x*

Percent increase = 25%

**Step 2:**

Increase in price = 25% of *x* = 0.25 × *x* = 0.25*x*

Final amount = Original amount + increase = *x* + 0.25*x* = 1.25*x*

**Step 3:**

Final amount = $750 = 1.25*x*

Solving for *x*

*x* = $\frac{750}{1.25} =$ $600

So, original amount = $600

After a 60% discount, a lawn chair was $105. Find the original price

### Solution

**Step 1:**

Let the original amount be = *x*

Percent increase = 60%

**Step 2:**

Decrease in price = 60% of *x* = 0.60 × *x* = 0.6*x*

Final amount = Original amount − Decrease = *x* − 0.6*x* = 0.4*x*

**Step 3:**

Final amount = $105 = 0.4*x*

Solving for *x*

*x* = $\frac{105}{0.4} =$ $262.50

So, original amount = $262.50