Question

three bulbs flash at the interval of 120 seconds,72 seconds and 13 seconds resspectively.Now suppose the three bulbs flash simultaneously at 8:00:00 on clock that loses two seconds every minute according to the same watch when will they flash simultaneously again?​

Answer 1

Given:

There are three bulbs which flash after each 120 seconds, 72 seconds and 13 seconds respectively. In a clock the three bulbs flash simultaneously at 8:00:00. And the clock loses 2 seconds every minute.

To Find:

We have to find, in the same clock when will the three bulbs flash simultaneously again

Step-by-step explanation:

The three bulbs will flash again together at the same time after the least common multiple (L.C.M.) seconds of 120 seconds, 72 seconds and 13 seconds.

Now, the L.C.M. of 120, 72 and 13 is 4680.

Now, 4680 seconds is equivalent to 78 minutes that means 1 hour 18 minutes.

Again, the clock will loose $(2\times 78) = 156 \textrm { seconds} = 2 \textrm { minutes } 36 \textrm { seconds}$

Therefore, the bulbs will flash simultaneously again at $[8 \textrm{ hr} + 1\textrm{ hr }18\textrm{ mins }-2\textrm { mins }36 \textrm{ secs}] = 9 \textrm{ hr }15\textrm{ mins }24 \textrm { secs }$

i.e. at 9:15:24 on clock.