A bus travels 2/5 of a total journey at its usual speed. The remaining distance was covered by bus at 6/7 of its usual speed. Due to slow speed it reaches its destination 50 minutes late. If the total distance is 200 kms, then what is the usual speed (in km/hr) of bus?

Let the usual speed of bus = $$7x$$ km/hr

Total distance = 200 km

Distance travelled at usual speed = $$\frac{2}{5}\times200=80$$ km

and distance travelled at slow speed = $$200-80=120$$ km

Slow speed = $$\frac{6}{7}\times7x=6x$$ km/hr

According to ques,

=> $$\frac{120}{6x}-\frac{120}{7x}=\frac{50}{60}$$

=> $$\frac{20}{x}-\frac{120}{7x}=\frac{5}{6}$$

=> $$\frac{20}{7x}=\frac{5}{6}$$

=> $$x=\frac{20}{7}\times\frac{6}{5}=\frac{120}{35}$$

$$\therefore$$ Usual speed of bus = $$7\times\frac{120}{35}=24$$ km/hr

=> Ans - (A)