Question

five guns are fired at intervals of 2,3,5,6 and 10 seconds respectively. at what intervals they be fired together and how many times will each be fired during that time?

Answer 1

Five guns are fired at interval 2 , 3 , 5 , 6 and 10 second .

intervals in which they be fired together = LCM { 2, 3 , 5 , 6, 10 }

so, LCM { 2 , 3 , 5 , 6 , 10} = 30

hence, time intervals = 30 second in which they be fired together.

no of firing by gun = time interval in which they fired together /time interval they fired individual .
so,
for First gun
number of firing = 30/2 = 15

for second gun
number of firing = 30/3 = 10

for 3rd gun
number of firing = 30/5 = 6

for 4th gun
number of firing = 30/6 = 5

for 5th gun
number of firing = 30/10 = 3

Answer 2

first we have to find the LCM of 2,3,5,6,10
LCM of these numbers is 30

they fired together in 30 sec

1 bell fired = 30/2=15 times
2 bell fired= 30/3 =10 times
3bell fired= 30/5= 6 times
4 bell fired= 30/6= 5 times
5bell fired = 30/10 = 3 times