Verbal Reasoning - Arithmetic Reasoning - Discussion

Why multiply by 7*8 and so on? Please tel me.

I also want to know why 7*8 and 7*9 are multiplied ?

One hr means 60 min & according to given condition (how many times will they toll together in one hr excluding start one).

So they can toll together in one hr excluding start one is 8 times.

(Because one toll together in 7 min i.e. max toll together excluding start one is 60/7 = 8.57).

8 is the answer because 7* 8 does not exceed 60 mins but 7 * 9 exceeds 60 mins. So from this, 8 is the answer.

If we had to find the answer considering the starting toll too. What would be the answer and how would we find out?

1 hour = 60 minutes.
1 minutes = 60 seconds.

So 60 minutes = 60*60 = 3600 seconds.
The last interval is 12 seconds so 3600/12 =300.

It will give the seconds of last bell ringing in sequence.
Now 300/3600*100 = 8.33.

So 8 minutes is the answer.

How did we exclude the bell tolled at the first time while getting the answer as 8 times?

Five bells begin to toll together means: when they begin they toll together.

Then at intervals of 6, 5, 7, 10 and 12.

The only way to know when will they again toll together is by taking LCM (least common multiple).

LCM of 6, 5, 7, 10 and 12 is 420 seconds.

As 1 min = 60 seconds.

So 420/60 = 7 minutes.

So, the bells will toll together after every 7 minutes.

That means 1st at 7 minutes; next at 14 minutes; next at 21 minutes and so on.

Means in 1 hour if I want to calculate how many times then it will be 8 times.

As total time (60 mins) = no. of times X 1 time (7 minutes).

Or no. times they will toll together = Total time/1 time.

i.e 60/7 = 8 times (approx).

If it asks for including the beginning when they start to toll together; then it will be,

8 times + 1 time = 9 times (remember as question said that they start by tolling together then they toll in intervals of 6, 5, 7, 10 and 12 seconds).

It tolls together 9 times.
It is;

1starting
2nd on 7
3rd on 14
4th on 21
5th on 28
6th on 35
7th on 42
8th on 49
9th on 56 minutes.

What does it mean at the interval of 6, 5, 7, 10, 12 and why we are taking lcm?

Please explain it to me.