## Tuesday, 22 November 2011

### Arithmetic-20 (FMS-2011)

The times between 7 and 8’O clock, correct to the nearest minute, when the hands of a clock will form an angle of 84 degrees are:
(1)7:23 and 7:53       (2)7:20 and 7:50       (3)7:22 and 7:53
(4)7:23 and 7:52
Solution follows here:
Solution:
Concept on clocks:
Speed of minutes hand = 3600 per hour = 60 per minute
Speed of hours hand = 300 per hour = 0.50 per minute
Relative speed of minutes hand over hours hand = 5.50 per minute
If time is expressed as h:m, to find angle between minutes and hours hands:
At time h:0, angle between minutes and hours hands = 30h
After m minutes, ie., at h:m, minutes hand travels an angle of ‘5.5m’ relative to hours hand, and may or may not exceed the angle ‘30h’
=> the angle = 30h-5.5m (or) 5.5m-30h
If time is expressed as h:m, angle between minutes and hours hands
= 30h-5.5m (or) 5.5m-30h
Here, Angle = 84;      h = 7
84 = 30(7)-5.5m => m = 126/5.5 = 22.9 23
84 = 5.5m-30(7) => m = 294/5.5 = 53.45 53
∴ the times are 7:23 and 7:53