Question

The difference of two numbers is 1/9 of their sum sum of the numbers is 45 Find thier HCF


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Answer 1

Answer:

1/9

Step-by-step explanation:

Let the two no.s be x & y

Given:

x - y = 1/9 ------Eqn 1

x + y = 45 ------Eqn 2

To Find:

HCF (x,y)

Solution:

x = 45 - y  ------- from Eqn 2

Substituting {x = 45 - y} in Eqn 1

45 - y - y = 1/9

45 - 2y = 1/9

2y = 45 - 1/9

2y = (405-1)/9   ------Taking LCM

2y = 404/9

y = 404/(9x2)

y = 202/9

Substituting {y = 202/9} in Eqn 1

x - 202/9 = 1/9

x = 1/9 - 202/9

x = 203/9

HCF (x,y):

x = 202/9 = 2 x 101 / 9

y = 203/9 = 7 x 29 / 9

Numbers common in x & y is 1/9

Therefore, HCF (x,y) is 1/9