If a number x is increased by 20% and then reduced by 20 , it results in 160 .Instead , if the number x is rduced by 20% and increased by 20 then what will be the result?

Options

A. `140`
B. `144`
C. `148`
D. `152`

Explanation

To solve the problem step by step, let's follow the same approach as the video transcript:

### Step 1: Set up the equation for the first scenario
We know that when the number \( x \) is increased by 20% and then reduced by 20, it results in 160.

First, we calculate 20% of \( x \):
\[ 20\% \text{ of } x = \frac{20}{100} \times x = \frac{x}{5} \]

Now, when \( x \) is increased by 20%, it becomes:
\[ x + \frac{x}{5} = \frac{5x + x}{5} = \frac{6x}{5} \]

Next, we reduce this result by 20:
\[ \frac{6x}{5} - 20 = 160 \]

### Step 2: Solve the equation
Now, we will solve the equation:
\[ \frac{6x}{5} - 20 = 160 \]

Add 20 to both sides:
\[ \frac{6x}{5} = 160 + 20 \]
\[ \frac{6x}{5} = 180 \]

Now, multiply both sides by 5:
\[ 6x = 180 \times 5 \]
\[ 6x = 900 \]

Now, divide both sides by 6:
\[ x = \frac{900}{6} = 150 \]

### Step 3: Set up the equation for the second scenario
Now, we need to find the result when \( x \) is reduced by 20% and then increased by 20.

First, calculate 20% of \( x \):
\[ 20\% \text{ of } x = \frac{x}{5} \]

When \( x \) is reduced by 20%, it becomes:
\[ x - \frac{x}{5} = \frac{5x - x}{5} = \frac{4x}{5} \]

Now, we increase this result by 20:
\[ \frac{4x}{5} + 20 \]

### Step 4: Substitute the value of \( x \)
Now substitute \( x = 150 \):
\[ \frac{4 \times 150}{5} + 20 \]

Calculate \( \frac{4 \times 150}{5} \):
\[ \frac{600}{5} = 120 \]

Now add 20:
\[ 120 + 20 = 140 \]

### Final Result
The result when \( x \) is reduced by 20% and then increased by 20 is:
\[ \boxed{140} \]

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