Real numbers
Grade Class 10
Question:
<p>If the sum of LCM and HCF of two numbers is 1260 and their LCM is 900 more than their HCF, then the product of two numbers is</p>
<p style="display:inline">198400</p>
<p style="display:inline">194400</p>
<p style="display:inline">203400</p>
<p style="display:inline">205400</p>
Step-by-Step Solution
Key Concept: The product of two numbers is equal to the product of their HCF and LCM.
<p>Let the HCF of the numbers be x and their LCM be y.<br />
It is given that the sum of the HCF and LCM is 1260, therefore<br />
x + y = 1260 ....(i)<br />
And, LCM is 900 more than HCF.<br />
y = x + 900 ..... (ii)<br />
Substituting (ii) in (i), we get:<br />
x + x + 900 =1260<br />
<span class="math-tex">$\Rightarrow$</span> 2x + 900 = 1260<br />
<span class="math-tex">$\Rightarrow$</span> 2x = 1260 - 900<br />
<span class="math-tex">$\Rightarrow$</span>2x = 360<br />
<span class="math-tex">$\Rightarrow$</span> x = 180<br />
Substituting x = 180 in (i), we get:<br />
y = 180 + 900<br />
<span class="math-tex">$\Rightarrow$</span> y = 1080<br />
We also know that the product the two numbers is equal to the product of their LCM and HCF<br />
Thus, product of the numbers = 1080(180) = 194400</p>
Correct Answer: B