Question

Four balls roll together at 8:00 am. They roll after 7,8,11 and 12 seconds respectively. After how much time they roll together ?​

Answer 1

Given,

Four balls roll together at 8:00 am. They roll after 7,8,11 and 12 seconds respectively.

To Find,

After how much time they roll together.

Solution,

Time at which all the 4 balls roll together = 8:00 am.

Time after which the first ball will roll again = 7 s

Time after which the second ball will roll again= 8 s

Time after which the third ball will roll again= 11 s

Time after which the fourth ball will roll again = 12 s

Time at which the four balls will roll again together = LCM of 7, 8 , 11, 12

LCM of 7, 8, 11 and 12

7 = 1 x 7

8 = 2 x 2 x 2

11 = 1 x 11

12 = 2 x 2 x 3

Taking the common factors = 2 x 2 x 2 x 3 x 7 x 11 = 1848

Therefore the 4 balls will roll again together after 1848 seconds.

We know that:

1 min = 60 seconds

1848 seconds = 1848/60 = 31 mins 15 seconds

Therefore the balls will roll together at 8 hours 31 minutes and 15 seconds.

Formulas used,

→ LCM

→ Conversion of seconds into minutes