Kim and Om are travelling from points A to B, which are 400 km apart. Travelling at a certain speed Kim takes one hour more than Om to reach point B. If Kim doubles her speed she will take 1 hour 30 mins less than Om to reach point B. At what speed was Kim driving from point A to B ? (In kmph)

Answer: Option D

Let the speed of Kim be a and that of Om be b
Distance between point A and B = 400 km
Then,
$$\frac{400}{a}-\frac{400}{b}=1$$
Let,
$$\begin{array}{rl}& \frac{1}{a}=x\text{ and }\frac{1}{b}=y\\ & 400x-400y=\mathrm{1.....}(i)\end{array}$$
Speed of km doubles and she will take lets time i.e., 1 hr 30 min than 0 metre
Again,
$$\begin{array}{rl}& \frac{400}{b}-\frac{400}{2b}=\frac{3}{2}\\ & \therefore 400y-200x=\frac{3}{2}\\ & 800y-400x=3\end{array}$$
Solving (i) and (ii), we get
$$\begin{array}{rl}& 400x-400y=1\\ & \frac{-400x+800y=3}{400y=4}\\ & \therefore y=\frac{4}{100}=\frac{1}{100}\text{ km}\\ & \therefore b=100\text{ km}\\ & \text{Now,}\\ & \frac{400}{a}-\frac{400}{100}=4\\ & \text{or, }\frac{400}{a}\\ & \therefore a=80\text{ kmph}\end{array}$$