the price of mobile is first decreased by 20% and then increased by 10%. the net change in the price will be:

Correct option is D

Given:

Initial price of the mobile: P

Price decrease: 20%

Price increase: 10%

Solution:

Decrease the price by 20%:

​$$\text{New Price after 20\% decrease} = P - (20\% \times P) = P \times (1 - 0.2) = 0.8P$$

​​Increase the reduced price by 10%:

​$$\text{New Price after 10\% increase} = 0.8P + (10\% \times 0.8P) = 0.8P \times (1 + 0.1) = 0.8P \times 1.1 = 0.88P$$

​​Net change in price:

Net change = Final price − Initial price 

Net change= 0.88P−P = −0.12P

The net change in the price is a 12% decrease. 

Alternate Method: 

Net percentage change = $$x +y +\frac{x\times y}{100}$$ 

for decrease(-ve) = 20% , for increase(+ve) = 10% 

So, $$-20 +10+\frac{(-20) \times (10)}{100}$$

​$$=-10 - 2 = -12 \%$$ 

thus the price will decrease by 12%.