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?

Correct option is C

Given:
A number is first decreased by 10%, then increased by 30%, and finally decreased by 20%.

Formula Used:

Net Percentage Change = $$(1 - \text{First change}) \times (1 + \text{Second change}) \times (1 - \text{Third change}) - 1$$​

Net Percentage = $$\left[ (1 - \frac{10}{100}) \times (1 + \frac{30}{100}) \times (1 - \frac{20}{100}) - 1 \right] \times 100$$​​
Solution:
First decrease by 10%: 
After decrease = $$\left(1 - \frac{10}{100}\right) = 0.9$$​​
Increase by 30%: 
After increase = $$\left(1 + \frac{30}{100}\right) = 1.3$$​​
Further decrease by 20%: 
After decrease = $$\left(1 - \frac{20}{100}\right) = 0.8$$​​
Net change: ​$$0.9 \times 1.3 \times 0.8 = 0.936$$​​

Net change = $$(0.936 - 1) \times 100 = -0.064 \times 100 = -6.4\%$$

Thus, the net decrease is 6.4%.
The net decrease percentage is $$6 \frac{2}{5}\%.$$​​
Thus, the  correct option is (c) 

Alternate Method:

- 10% ; +30% ; -20%

Successive formula = $$\left(A + B + \frac{AB}{100}\right)\%$$​​

Net change in % (-10% and + 30%) = $$\left(-10 + 30 - \frac{300}{100}\right)\%$$ = 17%

Net change in % (17% and - 20%) = $$\left(17 -20 - \frac{340}{100}\right)\%$$ = -6.4% = $$6 \frac{2}{5}\%$$​​

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