Correct Answer - Option 3 : 60 km/h
Given:
Distance between Prayagraj And Lucknow is 200 kms.
Speed for first quarter of journey = 40 km/h
Speed for remaining three quarter of journey = x km/h
Average Speed of the entire Journey = 53.33 km/h
Formula Used:
\({\rm{Time}} = \frac{{{\rm{Distance}}}}{{{\rm{Speed}}}}\)
Calculation:
If total distance is 200 kms. then each quarter consists of distance of 50 kms.
We can equate the time taken with partial journey speed and average speed journey.
\({\rm{Total\;time\;taken}} = \frac{{50}}{{40}} + \frac{{150}}{x} = \frac{{200}}{{53.33}}\)
\( \Rightarrow \frac{{50{\rm{x}} + 6000}}{{40{\rm{x}}}} = \frac{{200}}{{53.33}}\)
\( \Rightarrow \left( {50{\rm{x}} + 6000} \right) \times 53\frac{1}{3}\; = 200 \times 40{\rm{x}}\)
\( \Rightarrow \left( {50{\rm{x}} + 6000} \right) \times \frac{{160}}{3} = 8000x\)
⇒ (8000x + 960000) = 24000x
⇒ 16000x = 960000
\( \Rightarrow {\rm{x}} = \frac{{960000}}{{16000}} = 60\)
∴ Value of x is 60 km/h.
