Question

An electronic devices make a beep after 15 min another device make a beep after 20 min they beep together at 6a.m. at what time will they next beep together

Answer 1

this is type of A.P.
arithmetic progression

for first atomic device
15 + (r-1)15
= 15r

for second
20 + (n-1)20
= 20n

where r and n are positive integers
and r and n are number of deep they made after 6a.m

so for next deep together
15r = 20n
3r = 4n

as r and n are integers
so
r = 4
and n = 3

i.e. they will deep together again
after 60min
or 1hr
or 7a.m.

ans = 7a.m.