The sum of two numbers is 216 and their H.C.F | vedclass

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Question

(C) Let the two numbers be $27a$ and $27b$,where $a$ and $b$ are co-prime numbers.Given that the sum of the numbers is $216$,we have:$27a + 27b = 216$

Vedclass · Accepted Answer

$27, 189$

Vedclass · Answer

(C) Let the two numbers be $27a$ and $27b$,where $a$ and $b$ are co-prime numbers.Given that the sum of the numbers is $216$,we have:$27a + 27b = 216$$27(a + b) = 216$$a + b = \frac{216}{27} = 8$Now,we find pairs of co-prime numbers $(a, b)$ such that their sum is $8$:Possible pairs are $(1, 7)$ and $(3, 5)$.For the pair $(1, 7)$,the numbers are $(27 	imes 1, 27 	imes 7) = (27, 189)$.For the pair $(3, 5)$,the numbers are $(27 	imes 3, 27 	imes 5) = (81, 135)$.Since $(27, 189)$ is given in the options,the correct answer is $(27, 189)$.

The sum of two numbers is $216$ and their $H.C.F.$ is $27$. The numbers are

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