A man cycles with a speed of 10 km h and reaches his offices at 1 pm However when he cycles with a s...........

Quant (SSC) Time & distance

A man cycles with a speed of 10 km/h and reaches his offices at 1 pm. However, when he cycles with a speed of 15 km/h, he reaches his office at 11 am. At what speed should he cycle, so that he reaches his office at 12 noon?

12.5 km/hr

12 km/hr

13 km/hr

13/5 km/hr

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Explanation:

Let the distance be x km. then,
Time taken by slower train – Time taken by faster train = Difference in time
x/10 - x/15 = 1 pm - 11 am
⇒ 3x - 2x /30 = 2
⇒ x = 60 km
At 10 km/hr speed a man takes 6 hr and reach at 1 pm
At 15 km/hr speed a man takes 4 hr and reach at 11 am
Similarly, to reach the destination at 12 pm (the mid value of the given points of time) he will take 5 hrs (the mid value of given periods of time).
So, the speed of the person = 60/5 = 12 km/hr