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# 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

E. None of these

Answer: Option C

### Solution(By Examveda Team)

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
Or, 25(4t + 3) = 136t
Or, 100t + 75 = 136t
Or, 36t = 75
Or, t = $$\frac{{75}}{{36}}$$ = 2.08 hours
Then, distance x km = 136 × 2.084 = 283.33 km.

## Comments ( 3 )

1. time deference =45min.=0.75hrs
1st train go in this period=100*.75=75km
now relative speed =(136-100)=36km/hr
so 2nd train meet each other time is=75÷36=2.08
distance is=136*2.08=283.33km

2. Simply you can use formua
Distance= (S1*S2*T) / (S1-S2)

where T= difference in time i.e. 45 min means 3/4 hrs. , S1 and S2 are speeds of given

3. Already 100 kmph train started before 136kmph train. So when time is taken into point where they meet the time taken by 100kmph train should be less than the other one. But u took in this way. Can u plz explaim???

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