Question : The total distance in a journey is 750 km. A bus travels the first 200 km at a speed of 40 kmph. Find the speed of the bus (in kmph) for the next 550 km such that the average speed of the bus is 50 kmph.
Option 1: 55
Option 2: 60
Option 3: 45
Option 4: 40
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Correct Answer: 55
Solution :
Let's denote the speed of the bus for the next 550 km be $x$
Average Speed $=\frac{\text{Total Distance}}{\text{Total Time}}$
For the first 200 km, the time taken ($t{_1}$) is given by:
⇒ $t{_1}=\frac{\text{Distance}}{\text{Speed}}=\frac{200}{40}=5$ hours
For the next 550 km, the time taken ($t{_2}$) is given by:
⇒ $t{_2}=\frac{\text{Distance}}{\text{Speed}}=\frac{550}{x}$ hours
Total Time taken$(T) =t{_1}+t{_2}$
$T =5+\frac{550}{x}$
Now, average speed $=\frac{750}{T}$
⇒ $50=\frac{750}{5+\frac{550}{x}}$
⇒ $50=\frac{750x}{5x+550}$
⇒ $50(5x+550)=750x$
⇒ $250x+27500=750x$
⇒ $500x=27500$
⇒ $x$ = 55 kmph
Hence, the correct answer is 55.
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