Number System
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Q.

The two positive integers '$p$' and '$q$' satisfy:

$dfrac{(p+q)}{t} = text{HCF}(p,q)$.

Which of the following two numbers sum up to '$t$'?

 A.

13 and 52

 B.

132 and 96

 C.

18 and 126

 D.

56 and 45

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Solution:
Option(D) is correct

Let $\text{HCF(p, q)} = H$

For two numbers $A$ and $B$, which are co-primes to each other.

We can represent $p$ and $q$ as
$p = H×A \text{ and } q= H×B$

So that $\dfrac{(p+q)}{t} =\text{ HCF(p, q)} = H$
⇒ $t = (A+B)$

Hence $t$ cab be represented as the sum of any two numbers which are co prime to each other.

Hence option(D) is correct choice.


(1) Comment(s)


Ravi
 ()

Where and how did we get that $t=a+b$?