Question

a train covers a certain distance at a uniform speed if the train would have been 10 kilometre per hour faster it would have taken 2 hours less than the scheduled time and if the train were slower by 10 km per hour it would have taken 3 hours more than the scheduled time find the distance covered by the train​

Answer 1

Given :-

• If the train would have been 10 kilometre per hour faster, it would have taken 2 hours less than the scheduled time.

• If the train were slower by 10 km per hour, it would have taken 3 hours more than the scheduled time.

To Find :-

• Distance covered by the train.

Solution :-

Let distance covered by the train be d km.

The speed and time of the train will be x km/h and t hours respectively.

We know,

$\bigstar\:\underline{\boxed{\bf{\blue{speed=\dfrac{distance\:travelled}{time\:taken}}}}}$

⟼ Distance, d = time (t)× speed ( x)

⟼ d = xt......... eq(1)

As per question :-

Given that,

If the train would have been 10 kilometre per hour faster, it would have taken 2 hours less than the scheduled time.

Therefore,

( x +10) ( t-2) = d

⟼ xt -2x +10t -20 = d

As we know that, d = xt ( From eq 1)

⟼ d -2x +10t -20 = d

⟼ -2x +10t = 20........... eq(2)

Again, it’s given that

If the train were slower by 10 km per hour, it would have taken 3 hours more than the scheduled time.

Therefore,

(x-10) (t+3) = d

⟼ xt + 3x -10t -30 = d

⟼ d +3x -10t -30 =d

⟼ 3x -10t =30......... eq(3)

Adding equation 2 and 3, we get

3x -10t =30

-2x +10t = 20

_____________

⟼ x =50

Now, put the value of x in eq(2)

-2x +10t = 20

⟼ -2 × 50 + 10t =20

⟼ t =12

Hence,

Speed of the train is = 50 km/h

Time taken by the train is = 12 hours

Therefore,

Distance, d = time (t)× speed ( x)

⟼Distance, d = 50 × 12

⟼Distance, d = 600 km

So, distance covered by the train is = 600 km