### Two trains for Mumbai leave Delhi at 6 am and 6.45 am and travel at 100 kmph and 136 kmph respectively. How many kilometers from Delhi will the two trains be together:

A. 262.4 km B. 260 km C. 283.33 km D. 275 km Answer: Option C
Difference in time of departure between two trains = 45 min. = $\frac{45}{60}$ hour = $\frac{3}{4}$ hour. Let the distance be x km from Delhi where the two trains will be together. Time taken to cover x km with speed 136 kmph be t hour and time taken to cover x km with speed 100 kmph (As the train take 45 mins. more) be $\begin{array}{l} t+\frac{3}{4} \\ =\frac{4 t+3}{4} \end{array}$ Now, $\begin{array}{l} 100 \times \frac{4 t+3}{4}=136 t \\ \text { Or, } 25(4 t+3)=136 t \\ \text { Or, } 100 t+75=136 t \\ \text { Or, } 36 t=75 \\ \text { Or, } t=\frac{75}{36}=2.083 \text { hours } \end{array}$ Then, distance x km = 136 × 2.083 ≈ 283.33 km.