correct answer is: c) 10 seconds

Explanation

First intervals of the bell is =3\large\frac{1}{3} or \large\frac{10}{3} second.
Second intervals of the bell is =2\large\frac{1}{2} or \large\frac{5}{2} second.
Third intervals of the bell is =1\large\frac{2}{3} or \large\frac{5}{3} second.
To find the required time we need to LCM the intervals.
We know,
The formula we use to get the LCM of two or more fractions is:
\large\frac{The\ LCM\ of\ Numerator}{The\ HCF\ of\ Denominator}
\therefore The LCM of the three intervals is:
\rightarrow LCM of Numerators 10, 5 and 4 is =10
\rightarrow HCF of Denominators 3, 2 and 3 is =1
So that, the LCM of 3\large\frac{1}{3}\normalsize,2\frac{1}{2},1\large\frac{2}{3} is =\large\frac{10}{1} or 10.
\therefore After 10 seconds the bells will toll together.
Ans: The bells will toll together again after 10 seconds.

There’s another way to pose this same math question:

1. Find the next time when three bells will toll together, given their intervals are 3 1/3, 2 ½ and 1 2/3 seconds.
2. Calculate the time when three bells will chime simultaneously again, with intervals of 3 1/3, 2 ½ and 1 2/3 seconds.
3. Find out when the three bells will toll together again, with intervals of 3 1/3, 2 ½ and 1 2/3 seconds respectively.
4. When will three bells toll simultaneously again, with intervals of 3 1/3, 2 ½, and 1 2/3 seconds?