Question

A train goes from Mumbai to Delhi at a
uniform speed. If the speed of the train is
increased by 46 km/hr, the time to reach
Delhi is reduced by 2 - hours. If the speed is
reduced by 46 km/hr, it takes 5 hours more
to reach Delhi. Find the speed of the train
and the distance between Mumbai and
Delhi.​

Answer 1

Answer:

The speed of train between Mumbai to Delhi is 46 km/h

The distance between Mumbai to Delhi is 184 km .

Step-by-step explanation:

Given as  :

The distance between Mumbai to Delhi = D km

Let The Usual speed of train = S km/h

Let The usual time to reach = T hours

If the speed of the train is  increased by 46 km/hr, the time to reach

Delhi is reduced by 2 hours.

∵ Distance = Speed ×Time

I.e D = S × T

Or D = (S + 46 ) × (T - 2)

Or, ST = ST - 2 S + 46 T - 92

Or, 2 S - 46 T + 92 = 0                .......A

Again

If the speed is  reduced by 46 km/hr, it takes 5 hours more

to reach Delhi.

Or, D = (S - 46 ) × (T + 5)

Or, ST = ST + 5 S - 46 T - 230

Or, - 5 S + 46 T + 230 = 0           ...........B

Solving eq A and eq B

( 2 S - 46 T + 92 ) + ( - 5 S + 46 T + 230 ) = 0

Or, ( - 2 S - 5 S ) + ( - 46 T + 46 T ) + ( 92 + 230 ) = 0

Or, - 7 S + 0 + 322 = 0

Or, S = $\dfrac{322}{7}$

i.e S = 46 km/h

So, The speed of train between Mumbai to Delhi is 46 km/h

Put The value of S in eq A

2 × 46 - 46 T + 92 = 0  

Or, 46 T= 184

∴  T = $\dfrac{184}{46}$

i.e T = 4 hour

So, The time taken by train is 4 hours

Again

Since Distance = Speed × Time

So, Distance = 46 km/h × 4 h

∴   Distance = 184 km

Hence, The speed of train between Mumbai to Delhi is 46 km/h

And The distance between Mumbai to Delhi is 184 km . Answer