Question

if a train runs at 40kmph it reaches its destination late by 11 minutes. but if it runs at 50kmph it is late by 5 minutes only.find the distance to be covered by the train?

Answer 1

Let us consider the time of journey be T hrs
then,as distance is same, then
A/Q,
⇒40( T +11/60) =50 (T- 5/60)
⇒T= 23/30 hr
distance= speed ×time
              = 40×23/30
              =92/3 km
              =30.66 km

Answer 2

Answer:

Given :

Speed of train is $\display \text{40 km/hr}$ and its late by 11 min or $\displaystyle{\dfrac{11}{60} \ \text{hr}}$ .

In other case it's also given speed of train is $\display \text{50 km/hr}$ and late by 5 min or $\displaystyle{\dfrac{5}{60} \ \text{hr}}$.

Let the train covered 'd' km distance.

The journey let it took 't' hr time.

We have difference in late of time i.e.

$\displaystyle{\dfrac{11}{60} -\dfrac{5}{60}=\dfrac{1}{10}}$

We know ,

$\display \text{Time = \dfrac{\text{Distance}}{\text{Speed}} }$

A.T.Q.

$\displaystyle{\frac{\text{d}}{40} -\frac{\text{d}}{50}= \frac{1}{10}}\\\\\\\displaystyle{\dfrac{\text{d}}{10}\left(\frac{1}{4} -\frac{1}{5}\right)= \frac{1}{10}}\\\\\\\displaystyle{\text{d}\left(\dfrac{1}{20}\right)=1}\\\\\\\displaystyle{\text{d}=20 \ \text{km}}$

Hence , the distance to be covered by the train is 20 km .