Question

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 Lucknow and Delhi?

Answer 1

Consider the speed of train as x
 and the time taken by train as y

As we know: Distance(D) = Speed × Time
 then Distance will be x × y = xy
 Now,
If Rajdhani would have run slower by 10 km/h it will be (x-10)
It would have taken 3 hrs more to reach destination it will be (y+3)
1st Equation is
(x-10) (y+3) = xy
xy+3x-10y-30 = xy       (xy will be canceled on both sides)
then the eq. will be;
3x-10y-30 = 0 ⇒ 1st Equation

If Rajdhani would have run faster by 10km/h it will be (x+10)
it would have taken 2hrs less it will be (y-2)
2nd Equation is
(x+10) (y-2) = xy
xy-2x+10y-20 = xy     (xy will be canceledon both sides)
-2x+10y-20 = 0 ⇒ 2nd Equation

For further solution Add these 2 equation:
 3x -10y-30 = 0
-2x+10y-20 = 0
------------------------
x-50 = 0
therefore x= 50 (hence uniform speed of train is 50)

For the value of y apply the value of x on 1st equation::
3x - 10y - 30 = 0
3 × 50 - 10y - 30 = 0
150 -10y -30 = 0
120 - 10y = 0
-10y = -120
∴ y= 12 (average time taken by rajdhani to reach destination.

Distance = speed × time
50 × 12 = 600 Km

∴ The distance between Lucknow to Delhi is 600 Km.