Question

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

Answer 1

Answer:

the pairs of numbers are 18,117; 36, 99; 63, 72.

Answer 2

The sum of two numbers is 135 and their HCF is 9. There are 4 such pairs can be formed

Solution:

Given, the sum of two numbers is 135 and their HCF is 9.  

We have to find how many such pairs of numbers can be formed

Now, as HCF is 9. Let the numbers be 9x and 9y

Then, sum = 135

9x + 9y = 135

9(x + y) = 135

x + y = 15

Now, pair of possible values of x and y are

(1, 14), (2, 13), (3, 12), (4, 11), (5, 10), (6, 9), (7, 8).

Now, we can neglect some of the above pairs which has common factors as if they have common factor, HCF of 9x and 9y changes.

So, (1, 14), (2, 13), (4, 11), (7, 8)

Then, pair of numbers of 9x and 9y are (9, 126), (18, 117), (36, 99), (63, 72).

Hence, 4 such pairs can be formed.