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Question:

A chartered bus carrying office employees travels everyday in two shifts- morning and evening. In the evening, the bus travels at an average speed which is 50% greater than the morning average speed; but takes 50% more time than the amount of time it takes in the morning. The average speed of the chartered bus for the entire journey is greater/less than its average speed in the morning by:

Explanation:

Let the bus travels at speed ‘V’km/hr for time ‘T’ hours in the morning.

∴ Distance travelled in the morning = VT km

∴ In the evening, it travels at speed ‘1.5V’km/hr for ‘1.5T’ hours respectively.

∴ Distance travelled in the evening = 1.5V × 1.5T = 2.25VT

∴ Average speed = $\frac{T o t a l D i s \tan c e}{T o t a l T i m e}$

$= \frac{(V T + 2.25 V T)}{(T + 1.5 T)}$

$ = \frac{3.25 V}{2.5} = 1.3 V$

∴ The average speed of the chartered bus for the entire journey is greater than its average speed in the morning by 30%.

Hence, option (b).

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