Question

The train travels $300$ km at uniform speed. If the speed had been $10$ km/hr more, it would have take $1$ hour less for the same journey. Find the speed of the train.

• A. $60km/hr$
• B. $50km/hr$
• C. $40km/hr$
• D. $30km/hr$

Answer 1

Answer: (B)

$50km/hr$

Let the speed of train be $x$ $km/h$

Let the time taken be $t$ $hrs$

$\therefore xt=300km$

If speed is $(x+10)$ $km/h$

Then time is $(t-1)$ h

$(x+10)(t-1)=300$

$xt-x+10t-10=300$

$\frac{-300}{t}+10t-10=0$

$-300+10t^2-10t=0$

$t^2-t-30=0$

$t^2-6t+5t-30=0$

$t(t-6)+5(t-6)=0$

$(t-6)(t+5)=0$

$t=6$ hours

$x=50$ $km/h$