a) 262.4 km
b) 260 km
c) 283.33 km
d) 275 km
Answer: c
Explanation: 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
$$ {{\text{t}} + \frac{3}{4}} $$
= $$ {\frac{{4{\text{t}} + 3}}{4}} $$
Now,
100 × $$ {\frac{{4{\text{t}} + 3}}{4}} $$ = 136t
25(4t + 3) = 136t
100t + 75 = 136t
36t = 75
t = $$\frac{{75}}{{36}}$$ = 2.083 hours
Distance x km = 136 × 2.083 ≈ 283.33 km.
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