Question

11. Four bells toll at an interval of 4,7,12 and 84 seconds. The bells toll together
morning. When will they again toll together? How many times will they do se
nds. The bells toll together at 5 o'clock in the
How many times will they do so in 28 minutes?

Answer 1

They will toll together for a 'common multiple' of (4,7,12,84), which is the l.c.m of these numbers.

4== 2^2

7 == 7

12 = 2^2 * 3

84 = 12 * 7 = 2^2 * 3 * 7

l.c.m(4,7,12,84) = 2^2 * 3 * 7 = 84 s

84 s = 1 min 24 sec

Hence they will toll together 84 seconds after 5 o'clock or 5:01:24 hrs ( 1 min 24 sec past 5 o'clock)

28 mins = 28*60 = 1680 sec

84 sec== toll 1 time

1680 sec== X times

X = 20 times

Hence,

They toll together at 5:01:24 hrs

In 28 mins they toll (together) 20 times.

Hope it helps.