Real numbers
Grade Class 10
Question:
<p>In a seminar the number of participants in Mathematics, Physics and Biology are 192, 240 and 168. Find the minimum number of rooms required, if in each room same number of participants is to be seated and all of them being in the same subject.</p>
<p style="display:inline">30</p>
<p style="display:inline">20</p>
<p style="display:inline">28</p>
<p style="display:inline">25</p>
Step-by-Step Solution
Key Concept: To minimize the total number of rooms, maximize the participants per room by finding the HCF of the subject totals and then sum the quotients obtained by dividing each total by that HCF.
<p>H.C.F. of (192, 240, 168) = 2 <span class="math-tex">$\times$</span> 2<span class="math-tex">$\times$</span>2 <span class="math-tex">$\times$</span> 3 = 24<br />
Number of rooms for participants in Mathematics, Physics<br />
and Biology respectively is<span class="math-tex">$\frac{192}{24}, \frac{240}{24}$</span>and<span class="math-tex">$\frac{168}{24}$</span><br />
i.e., 8, 10 and 7<br />
<span class="math-tex">$\therefore$</span>Total minimum number of required rooms = 8 + 10 + 7 = 25</p>
Correct Answer: D