The HCF of two numbers is 11

The HCF of two numbers is 11 and their sum is 132. If both the numbers are greater than 42, then the difference between the two numbers is:
दो संख्याओं का HCF, 11है और उनका योग 132 है। यदि दोनों संख्याएँ 42 से बड़ी है, तो दोनों संख्याओं के बीच का अंतर ज्ञात कीजिए।

18 22 26 11

Detailed Solution & Logic

Correct Answer:

22

Let the two numbers be $11x$ and $11y$.
HCF $=11 (x,y)=1$
Given sum:
$11x+11y=132$
$11(x+y)=132 x+y=12$
Co-prime pair: $(x,y)=(5,7)$
Numbers:
$11\times5=55,11\times7=77$
Difference:
77-55=22
Answer = 22

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