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

Answer (1)