Question

Four different electronic devices make a 1 beep after every $30$ minutes. $1$ hour, 1 $\frac{1}{2}$ hour and $1$ hour $45$ minutes respectively. All the devices beeped together at $12$ noon. They will again beep together at:

• A. $12$ midnight
• B. $3$ a.m.
• C. $6$ a.m.
• D. $9$ a.m.

Answer 1

Answer: (D)

$9$ a.m.

First device beeps in every $30min$

Second device beeps in every $60min$

Third device beeps in every $90min$

Fourth device beeps in every $105min$

That means together they beep after how many minutes

We calculate $LCM(30,60,90,105)$

$30=2\times 3\times 5$

$60=2\times 2\times 3\times 5$

$90=2\times 3\times 3\times 5$

$105=3\times 5\times 7$

So, $LCM=2^2\times 3^2\times 5\times 7=1260$

$\Rightarrow$ ie, in $\frac{1260}{60}=21hrs$ they beep together.

$\Rightarrow$ All beeped together after 12 noon at 21 hrs later. i.e, $(12+21)hrs=9a.m.$

$\therefore$ Next they will beeped together at $9a.m.$