A number is first decreased by 10%, then increased by 30% and then further it is decreased by 20%. What is the net decrease percentage in the number?

The correct answer is 6.4%.

Step-by-Step Explanation:

Let the initial number be $x=100$.

Step 1: Decrease the number by 10%

$\text{Value after 10\% decrease}=100\times (1-\frac{10}{100})$

$=100\times 0.90=90$

Step 2: Increase the result by 30%

$\text{Value after 30\% increase}=90\times (1+\frac{30}{100})$

$=90\times 1.30=117$

Step 3: Decrease the result by 20%

$\text{Final value after 20\% decrease}=117\times (1-\frac{20}{100})$

$=117\times 0.80=93.6$

Step 4: Calculate the net decrease percentage

$\text{Net decrease}=\text{Initial Value}-\text{Final Value}$

$=100-93.6=6.4$

$\text{Net decrease percentage}=\left(\frac{6.4}{100}\right)\times 100\%=6.4\%$

Thus, the net decrease percentage in the number is 6.4%.