Question

5 bells commence tolling together at intervals of 4, 6, 5, 9, and 10 seconds respectively. In 30 minutes, how many times do they toll together? (Excluding the one at the start)
Please give a proper step by step explanation

Answer 1

Answer:

First bell rings at 4s

Second bell rings at 6s

Third bell rings at 5s

Fourth bell rings at 9s

Fifth bell rings at 10s

So, the solution look like this

⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️

Step-by-step explanation:

First take the L.C.M. of those numbers

• which is 180

• then it means 180s = 3 minutes

Now, we find how many times do the all bell rings together in 30 minutes.

TOTAL TIME

LCM OF SECONDS

= 30 minutes

180s or 3 minutes

= 30 minutes

3 minutes

= 10 minutes

• Hence, all five bells toll together 10 times in 30 minutes

Answer 2

Answer:

4 = 2x2

6 = 2x3

5 = 5x1

9= 3x3

10= 2x5

LCM = 2x2x3x3x5 = 180 sec

180 sec = 180/60 min. = 3 min.

for 1 time = 3 min

for 10 times = 30 min.