If the sum of two numbers is 430 and their HCF is 43, then which of the following is the correct pair?

The sum of two numbers is 430.

The HCF of the two numbers is 43.

If two numbers have an HCF of 43, then they can be expressed as 43x and 43y, where x and y are coprime integers (i.e., their HCF is 1). The sum of the two numbers is given by:

43x + 43y = 430

x + y = $$\frac{430}{43}$$​ = 10

Now,

Possible pairs (x, y) that satisfy x + y = 10 are:

(1, 9), (3, 7), (7, 3), (9, 1)

Now, multiplying each of these pairs by 43 gives the corresponding pairs for the original numbers:

(1×43, 9×43) = (43, 387)

(3×43, 7×43) = (129, 301)

(7×43, 3×43) = (301, 129)

(9×43, 1×43) = (387, 43)

Thus, The correct pair that appears in the options is: B. 129, 301