Question

Six strings of violin start vibrating simultaneously and they vibrate at, $3,4,5,6,10,and12$ times in a minute, find
i After how much time will all six of them vibrate together ?
ii. How many times will they vibrate together in $30$ min ?

• A. $60$ sec,$31$ times
• B. $60$ min, $31$ times
• C. $120$ sec, $15$ times
• D. None of these

Answer 1

The correct option is A $60$ sec,$31$ times

i After how much time will all six of them vibrate together ?
The LCM of $3,4,5,6,10,12$ will be time they will vibrate together. The LCM is $60$ . So, they will vibrate together after $60$ sec.
ii. How many times will they vibrate together in $30$ min ?
If they vibrate together after every minute, in $30$ minutes, they will vibrate $30$ times. But they start vibrating together, so it is $31$ times in $30$ minutes.