7

Part of 2019 India PRMO

Problems(2)

Hands of clock at 90 degrees

Source:

On a clock, there are two instants between

12

1 \,\mathrm{PM}

, when the hour hand and the minute hannd are at right angles. The difference in minutes between these two instants is written as

a + \dfrac{b}{c}

a, b, c

are positive integers, with

b < c

b/c

in the reduced form. What is the value of

a+b+c

Clock Problemsprmo 2k19

Source: PRMO 2019 Leg 2 P7

s(n)

denote the sum of digits of a positive integer

n

10

s(m)=20

s(33m)=120

, what is the value of

s(3m)

algebraPRMOnumber theorydecimal representation