a number is increased by 20% and the increased number is decreased by 20% find the net increase or decrease per cent

Answer

To solve the problem step by step, we will follow the process outlined in the video transcript.

### Step 1: Assume the Original Number
Let's assume the original number is \( 100 \).

### Step 2: Calculate the Increased Number
The number is increased by \( 20\% \). To find \( 20\% \) of \( 100 \):
\[ 20\% \text{ of } 100 = \frac{20}{100} \times 100 = 20 \]
Now, add this increase to the original number:
\[ 100 + 20 = 120 \]
So, the increased number is \( 120 \).

### Step 3: Calculate the Decreased Number
Next, we need to decrease the increased number \( 120 \) by \( 20\% \). First, find \( 20\% \) of \( 120 \):
\[ 20\% \text{ of } 120 = \frac{20}{100} \times 120 = 24 \]
Now, subtract this decrease from the increased number:
\[ 120 - 24 = 96 \]
So, the decreased number is \( 96 \).

### Step 4: Determine the Net Change
Now we need to find out whether there is a net increase or decrease. The original number was \( 100 \) and the final number after the increase and decrease is \( 96 \).

To find the net change:
\[ \text{Net Change} = \text{Old Value} - \text{New Value} = 100 - 96 = 4 \]

### Step 5: Calculate the Percentage of the Net Change
Now, we will calculate the percentage decrease using the formula:
\[ \text{Percentage Decrease} = \left( \frac{\text{Net Change}}{\text{Old Value}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Decrease} = \left( \frac{4}{100} \right) \times 100 = 4\% \]

### Conclusion
Thus, the net result is a decrease of \( 4\% \).

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