Question : The sum of the two numbers is 1224 and their HCF is 68. The number of pairs of numbers satisfying the above condition is:
Option 1: 3
Option 2: 4
Option 3: 6
Option 4: 2
Correct Answer: 3
Solution :
Given: The sum of the two numbers is 1224 and their HCF is 68.
Let the two numbers be $68x$ and $68y$.
According to the question,
$68x + 68y=1224$
⇒ $x+y=18$
So, the possible pairs of values which are co-prime to each other are (1, 17), (5, 13), and (7, 11).
$\therefore$ Number of required pairs is 3.
Hence, the correct answer is 3.
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