Question

On a clock, there are two instants between 12 noon and 1 PM, when the hour hand and

the minute hand are at right angles. The difference in minutes between these two instants is

written as a +

b

c

, where a, b, c are positive integers, with b < c and b/c in the reduced form. What

is the value of a + b + c ?​

Answer 1

Given:

Number of instants = 2

Hour and minute hand angle = right

Difference between two instants = a + b/c

To Find:

Value of a + b + c

Solution:

1st case -  

Angle between the hands  

θ = 11/2m - 30h = 90°

11/2m = 90 °

m = 180/11

2nd case -

θ = 11/2m - 30h = 270°

11/2m = 270°

m = 540/11

Therefore,  

540/11 - 180/11

= 360/11

= 32 + 8/11 = a +b/c

= a + b + c = 32 + 8 + 11

=  51

Answer: The value of a + b + c is 51.