Question

The sum of two numbers is 684 and their HCF is 57. Find all possible pairs of such numbers.
A.(57,627)(285,399)
B.(37,575)(270,390)
C.(45,495)(30,330)
D.(45,575)(280,890)

Answer 1

Since, HCF of two numbers = 57.
Hence, numbers are multiples of 57.
Let, the numbers be 57x and 57y, where x and y are prime to each other.
According to the sum,
57x+57y = 684;
Or, x+y = 12;
Hence, required possible pair of values of x and y which are prime to each other are (1, 11) and (5, 7).
Thus, required pairs of numbers are;
{57*1 = 57 and 57*11 = 627}

{57*5 = 285 and 57*7 = 399 }