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

Correct option is B

Given:

Sum of two  numbers = 430

HCF of two numbers  = 43

Formula Used:

Product of two numbers = HCF $$\times$$​ LCM

Solution:

Let the numbers be x and y

Then x + y = 430

Also their HCF is 43 then let co-prime numbers a and b then,

x= 43a and y = 43b

(43a +43b) = 430

43(a+b) = 430

a+b = 10

The number of pairs for a and b are (1,9),(3,7)

Hence the number can be from pair one = $$(1 \times 43, 9 \times 43)$$​ = (43, 387)

The number can be from pair second =$$(3 \times 43, 7 \times 43)$$​ = (129, 301)

Option(b) is correct