a) 50 sec

b) 48 sec

c) 42 sec

d) 40 sec

Correct answer is: c) 42 sec

#### Explanation

Five bells begin to toll at the intervals of 1\large\frac{1}{5}\normalsize,1\large\frac{1}{2}\normalsize,1\large\frac{3}{4}\normalsize,1\large\frac{2}{5}\normalsize,2\large\frac{1}{10} sec.

Or, \large\frac{6}{5},\frac{3}{2},\frac{7}{4},\frac{7}{5},\frac{21}{10} sec _{[covert mixed to improper]}

To, find the required time when the bells toll together again, we need to find the LCM of \large\frac{6}{5},\frac{3}{2},\frac{7}{4},\frac{7}{5},\frac{21}{10} *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}

\rightarrow LCM of Numerators 6,3,7,7,21 =2\times3\times7=42

\rightarrow HCF of Denominators 5,2,4,5,10 is =2\times5=1

So that, the LCM of \large\frac{6}{5},\frac{3}{2},\frac{7}{4},\frac{7}{5} and \large\frac{21}{10} is =\large\frac{42}{1} or 42

\therefore The bells will toll together after 42 sec.**Ans:** After 42 second the bells will toll together.

###### An alternative way to phrase this particular math query is possible:

**After ringing together, five bells toll at intervals of 1 1/5 sec, 1 ½ sec, 1 ¾ sec, 1 2/5 sec, and 2 1/10 sec respectively. When will they toll together again?****Calculate the time at which five bells will ring together again, considering their intervals as 1 1/5 sec, 1 ½ sec, 1 ¾ sec, 1 2/5 sec, and 2 1/10 sec respectively.****Find the next instance when all five bells will toll simultaneously, given that their intervals are 1 1/5 sec, 1 ½ sec, 1 ¾ sec, 1 2/5 sec, and 2 1/10 sec respectively.****Determine the moment when all five bells will ring in unison again, considering their intervals as 1 1/5 sec, 1 ½ sec, 1 ¾ sec, 1 2/5 sec, and 2 1/10 sec respectively.**