Question

Six strings of violin start vibrating simultaneously and they vibrate at 3, 4, 5, 6, 10 and 12 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

The six strings will vibrate together at multiples of the time taken by them to complete $1$ vibration.

I.E, LCM of their times.

LCM of $3,4,5,6,10,12=60$, hence they will vibrate together in every $60$ sec.

$1$ min = $60$ secs, i.e. in $30$ mins, they will vibrate $31$ times.