Question

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दो संख्याओं का योग 216 है तथा उनका म. स. 27
है, ऐसी सह अभाज्य संख्याओं के कितने जोड़े होंगे?​

Answer 1

Since HCF is 27, the two numbers can be written as 27*x and 27*y, Where x and y are co-prime (in order to make sure that the HCF is 27).

Now, Sum of the numbers is 216.

=> 27*(x+y) = 216

=> x+y = 8 and x and y are co-prime

So, the following possibilities exist for x and y and the numbers(also we are not interested in order of x and y )

x,y ; 27*x,27*y

1,7 ; 27, 189

2,6 not possible not co-prime

3,5 ; 81,135

4,4 not possible

Others already covered since (x,y) = (y,x) for us

So, finally the 2 numbers can be (27,189) or (81,135)