A man travelled the first 200 km at a speed of 50 km/h. the next 300 km at a speed of x km/h and the final 280 km at a speed of 80 km/h. If his average speed for the whole journey is 52 km/h. Then we value of x is:

Correct option is C

Given:

Distance travelled by man at 50km/hr = 200km

Distance travelled by man at x km/hr = 300km

Distance travelled by man at 80km/hr = 280km

Average speed for whole journey = 52km/hr

Formula Used:

Time = $$\frac{Distance}{Speed}$$​​

Average Speed = $$\frac{Total \ Distance}{Total\ Time}$$​​

Solution:

Total distance = 200+300+280 = 780km

Total time taken for whole journey =$$\frac{780}{52}$$ = 15hrs

Time taken in first 200km =$$\frac{200}{50}$$​= 4hr

Time taken in last 280km = $$\frac{280}{80}$$ = 3.5hrs

Total time left for 3^rd journey = 15 - (4 + 3.5) = 7.5

Speed of 3^rd journey of 300km at x =$$\frac{300}{7.5}$$ = 40km/hr