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16 May 2018 Speed and Distance

Veerbhadhran could either walk or drive to office. The time taken to walk to the office is 14 times the driving time. One day, his wife took the car making him walk to office. After walking 1 km, he reached a temple when his wife called to say that he can now take the car. Veerbhadhran figured that continuing to walk to the office will take half as long as walking back home and then driving to the office. Calculate the distance between the temple and the office in KMs.

OPtion

1) 14/9
2) 5/9
3) 11/9
4) 13/9
5) 10/9
6) 17/9
7) 16/9
8) 8/9
9) 7/9
10)None of these

Solution

Suppose the distance between his home and office is x km. Then, distance between his office and temple is (x – 1) km.
If he walks at a speed of y km/hr. Then his driving speed = 14y km/hour, as he is 14 times faster in car.

Then,
Time Taken To walk back Home from temple + Time Taken to drive to office from home = 2* Time taken to walk to office from temple
1/y + x/14y = 2*(x – 1)/y
Or, 1 + x/14 = 2x – 2
or 27x/14 = 3
Or, x = 14/9
Finally, x – 1 = 14/9 - 1 = 5/9
Option 2)

Correct Option: 2 Best Solution (0)