question_answer 51)

The traffic lights at three different road crossings change after every 48 seconds 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again?

Answer:

                The time period after which the traffic lights at three different road crossing changes simultaneously again will be the LCM of 48, 72 and 108. R 48, 36, 54 2 24, 36, 54 2 12, 18, 27 2 6, 9, 27 3 3, 9, 27 3 1, 3, 9 3 1, 1, 3 1, 1, 1 \[\therefore \] LCM \[=2\times 2\times 2\times 2\times 3\times 3\times 3=432\] \[=\frac{432}{60}\min =7\]minute 12 second           \[\left[ \begin{align}   & \because 1\min \,=60 \\  & \text{and1s=}\frac{1}{60}\min  \\ \end{align} \right]\] So, time when they will change again  \[\begin{matrix}    = & \begin{align}   & 07:00:00 \\  & \frac{+\,\,\,\,\,\,07:12}{07:07:12} \\ \end{align}  \\ \end{matrix}\] i.e. 7 min 12 s past 7 a.m.