Question

The sum of two digits is 324. Their HCF is 18. Find the difference between the two numbers.

Answer 1

Answer :

If the HCF if 18 , the numbers can be written as 18 x and 18 y, where x and y are co-prime to each other.

And sum of these two digits is 324 , So

18 x + 18 y = 324

18 ( x + y ) = 324

x + y = 18

The pair of numbers that are co-prime to each other and sum up to 18 are ( 1 , 17 ) , ( 5 , 13 ), ( 7 , 11 ) .

Hence, only three pairs of such numbers are possible. The numbers are ( 18 , 306 ), ( 90 , 234 ) and (126 , 198 ).

So,

Difference between 18 and 306 :

306 - 18 = 288 ,

Difference between 90 and 234 :

234 - 90 = 144

And

Difference between 126 and 198 :

198 - 126 = 72