Question

A cab has an average speed of 60 km/hr while going from Indore to Ujjain and has an average speed of X km/hr while returning the same distance from Ujjain to Indore. If the average speed of the cab for the whole journey is 48 km/hr, the value of X is
(A) 45 km/hr
(B) 40 km/hr
(C) 36 km/hr
(D) 30 km/hr

Answer 1

Answer:

36km/ hr

Step-by-step explanation:

X=60km/HR

let y=akm/HR

s=48km/HR

s=X+y/2

48=60+a/2

96-60=a

a=36

Answer 2

The correct option is B) 40 km/hr.

Step-by-step explanation:

Consider the provided information.

$Time=\frac{Distance}{Speed}$

Let the distance between Indore to ujjain is D.

A cab has an average speed of 60 km/hr while going from Indore to Ujjain

Therefore, the time taken is: $\frac{D}{60}$

While returning the same distance from Ujjain to Indore the average speed was x km/hr.

Therefore, the time taken is: $\frac{D}{x}$

The formula to calculate average speed is: $\text{Average speed}= \frac{\text{Total distance}}{\text{Elapsed Time}}$

Total distance is D+D=2D

$\text{Average speed}= \dfrac{2D}{\frac{D}{60}+\frac{D}{x}}$

It is given that Average speed is 48.

$48= \dfrac{2D}{\frac{D(x+60)}{60x}}$

$48= \dfrac{2}{\frac{x+60}{60x}}$

$48= \dfrac{120x}{x+60}$

$2(x+60)= 5x\\2x+120=5x\\3x=120\\x=40$

Hence, the correct option is B) 40 km/hr.

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