Question

6. Rajdhani train covered the distance between Lucknow and Delhi at a
uniform speed. It is observed that if Rajdhani would have run slower by
10 km/hr, it would have taken 3 hours more to reach the destination and if
Rajdhani would have run faster by 10 km/hr, it would have taken 2 hours
less. Find the distance between Lucknow and Delhi?​

Answer 1

Answer:

Distance between Lucknow and Delhi = 600 km.

Step-by-step explanation:

Let the speed of train be x km/hr and time taken be t hr.

So, Distance, D is given by = Speed * Time

             D   =  x * t ------ [Equation 1]

• First condition given is that if Rajdhani would have run 10 km/hr faster,it would have taken 2 hours less i.e.;

             D = (x + 10) * (t - 2)

              D = x * t - 2*x + 10*t - 20

               D = D - 2*x + 10*t - 20  {from equation 1}

                 10*t = 2*x + 20 --------- [Equation 2]

• Second condition given is that if Rajdhani would have run slower by    10 km/hr, it would have taken 3 hours more to reach the destination, i.e.;                 D = (x - 10) * (t + 3)

                              D = x * t + 3*x - 10*t - 30  

                              D = D + 3*x - 10*t - 30  {from equation 1}

                             3*x - 10*t - 30 = 0 --------- [Equation 3]

Now putting value of 10*t from equation 2 into 3 we get,

                         3*x - (2*x + 20) - 30 = 0

                           3*x - 2*x - 50 = 0

                            x = 50 km/hr

putting value of x in equation 2 we get, t = $\frac{2*50+20}{10}$ = 12 hr

Therefore, D = x * t = 50 * 12 = 600 km .

Answer 2

Answer:

Bro the answer is 600 km

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