'X' years ago, Rakesh's age was twice his brother's age and '4X' years ago, Rakesh's age was thrice his brother's age. If it is known that 'X' is a natural number, then what can be the absolute difference between their present ages? plz answer it fast it's urgent

The difference must be a multiple of 6

Step-by-step explanation:

R is Rakesh's age and B is the age of the brother.

the equations we have are:

(R - X) = 2*(B - X)

(R - 4X) = 3*(B - 4X)

where X must be a natural number.

we can write it as

(R - B) = -X + B

(R - B) = 2B - 8X

-X + B = 2B - 8X

B = 7X

then:

R - 7X = 6X

This means that the difference between their ages is a multiple of 6, for example, if the difference between them is 12 years, we have X = 2

R - 2 = 2*B - 4

R - 8 = 3*B - 24

in the first equation:

R = 2*B - 2

we replace it in the second eq:

2*B - 10 = 3*B - 24

B = 14 = 7*X = 7*2

and R = 14 + 12 = 26