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5 bells commence tolling together and toll at intervals 2, 4, 6, 8 and 10 seconds respectively. Find in 40 minutes, how many times do they toll together?

Question

5 bells commence tolling together and toll at intervals 2, 4, 6, 8 and 10 seconds respectively. Find in 40 minutes, how many times do they toll together?

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Solution

To solve this problem, we first need to find the least common multiple (LCM) of the intervals at which the bells toll. The intervals are 2, 4, 6, 8, and 10 seconds.

The LCM of 2, 4, 6, 8, and 10 is 120 seconds (or 2 minutes). This means that all the bells toll together every 2 minutes.

Next, we need to find out how many 2-minute intervals are there in 40 minutes. To do this, we divide 40 by 2, which gives us 20.

So, the bells toll together 20 times in 40 minutes.

However, we need to add 1 to this number because the bells also toll together at the start of the 40 minutes.

Therefore, the bells toll together 21 times in 40 minutes.

This problem has been solved

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