Question

Sum of two numbers is 400 and hcf is 25 how may such pairs exist

Answer 1

Since the HCF of two numbers is 25, let the numbers be 25x and 25y for two coprime integers x and y. Two integers are said to be coprime if their HCF is 1.

So that the sum is,

25x + 25y = 400

25 (x + y) = 400

x + y = 400 / 25

x + y = 16

So the possible values of the ordered pair (x, y) are taken in a set,

A = {(x, y) : x & y € N, x + y = 16, hcf(x, y) = 1}

as shown below in tabular form.

A = {(1, 15), (3, 13), (5, 11), (7, 9), (9, 7), (11, 5), (13, 3), (15, 1)}

Here the pairs in the form (x, y) are (y, x) are present, which are treated differently. So the total no. of possible pairs is given by,

n(A) / 2 = 8 / 2 = 4.

Hence 4 is the answer.

#answerwithquality

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