Question 6

The sum of two numbers is 135 and their HCF is 9. How many such pairs of numbers can be formed ?

Solution

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Let the two numbers be $$9x$$ and $$9y$$, where $$x$$ and $$y$$ are co prime numbers.

=> $$9x+9y=135$$

=> $$x+y=\frac{135}{9}=15$$

Now, pairs of natural numbers having sum 15 and co prime are = (1,14), (2,13), (4,11), (7,8)

Thus, 4 such pairs can be formed.

=> Ans - (C)

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