Real numbers
Grade Class 10
Question:
<p>Four different electronic devices make a beep after every 30 minutes, 1 hour,<span class="math-tex">\(1\frac {1} {2}\)</span>hour and 1 hour 45 minutes respectively. All the devices beeped together at 12 noon. They will again beep together at ________.</p>
<p style="display:inline">3 a.m.</p>
<p style="display:inline">12 midnight</p>
<p style="display:inline">9 a.m.</p>
<p style="display:inline">6 a.m.</p>
Step-by-Step Solution
Key Concept: The time until periodic events occur simultaneously again is the Least Common Multiple (LCM) of their individual time intervals.
<p>L.C.M. (30, 60, 90, 105) = 2<sup>2</sup><span class="math-tex">$\times$</span> 3<sup>2</sup> <span class="math-tex">$\times$</span> 5 <span class="math-tex">$\times$</span> 7<br />
= 1260 mins = 21 hours</p>
Correct Answer: C