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

(4)7:23 and 7:52

Solution follows here:

__Solution:__

__Concept on clocks:__
Speed of minutes hand = 360

^{0}per hour = 6^{0}per minute
Speed of hours hand = 30

^{0}per hour = 0.5^{0}per minute
Relative speed of minutes hand over hours hand = 5.5

^{0}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)**
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