The speed of a superfast train, $$T_{1}$$ is 20% more than the speed of another superfast train $$T_{2}$$. Both the trains start from point N at the same time and reach point M at the same time. N and M are 500 km apart. $$T_{1}$$ stops for 10 minutes on the way to M, but $$T_{2}$$ covers the distance without any stops in route. What is the speed of $$T_{1}$$?

The speed of a superfast train, $$T_{1}$$ is 20% more than the speed of another superfast train $$T_{2}$$.

Let's assume the speed of a superfast train $$T_{2}$$ is '5y' km/h.

speed of a superfast train $$T_{1}$$ = 120% of 5y

= $$\frac{120}{100}\times5y$$

= 6y

Both the trains start from point N at the same time and reach point M at the same time. N and M are 500 km apart. $$T_{1}$$ stops for 10 minutes on the way to M, but $$T_{2}$$ covers the distance without any stops in route.

Let's assume the time taken by each of them is 't' hours.

For superfast train, $$T_{1}$$

$$\frac{500}{6y}=\ \left(t-\frac{10}{60}\right)$$

$$500=\ 6yt-y$$    Eq.(i)

For superfast train, $$T_{2}$$

$$\frac{500}{5y}=\ t$$

$$yt = 100$$    Eq.(ii)

Put Eq.(ii) in Eq.(i).

$$500=\ 6\times100-y$$

$$y = 600-500 = 100$$

Speed of superfast train $$T_{1}$$ = 6y

= $$6\times100$$

= 600 km/h