A car is moving with a speed of 100 km/h. If the speed of car first increases by x% and then decreases by x%, the final speed of the car is 96 km/hr. The value of x is :

1. 4

2. 20

3. 8

4. 10

Given,

Initial speed = 100 km/hr

Increment = x%

Speed after increment = Initial speed + Increment

= 100 + $\dfrac{x}{100} \times 100$

= (100 + x) km/h.

Decrement = x%

Given,

Final speed = 96 km/hr

Final Speed = Speed after increment - Decrement

Substituting values we get :

$\Rightarrow 96 = 100 + x - \dfrac{x}{100} \times (100 + x) \\[1em] \Rightarrow 96 = 100 + x - x - \dfrac{x^2}{100} \\[1em] \Rightarrow 96 = 100 - \dfrac{x^2}{100} \\[1em] \Rightarrow \dfrac{x^2}{100} = 100 - 96 \\[1em] \Rightarrow \dfrac{x^2}{100} = 4 \\[1em] \Rightarrow x^2 = 400 \\[1em] \Rightarrow x = \sqrt{400} \\[1em] \Rightarrow x = 20.$

Hence, Option 2 is the correct option.