What should be subracted from both the numbers which are in the ratio 3:4 so that the ratio becomes 2:3?

What should be subracted from both the numbers which are in the ratio 3:4 so that the ratio becomes 2:3





a)4 b)6 c)10 d)cannot be determinedWhat should be subracted from both the numbers which are in the ratio 3:4 so that the ratio becomes 2:3?
Let the numbers be 3x and 4x


and number subtracted be y


3x 鈥?y/4x 鈥?y = 2/3


3(3x 鈥?y)/2(4x 鈥?y)


9x 鈥?3y = 8x 鈥?2y


y = x


can not be determined


-------------What should be subracted from both the numbers which are in the ratio 3:4 so that the ratio becomes 2:3?
Assuming that the two numbers are positive integers a, b, you'd have to subtract their greates common divisor:





Write them in the form a=3x, b=4x. Then x = gcd(a,b), and the only value y with the property (a-y)/(b-y) = 2/3 is y=x as has been pointed out by Pranil already:





(a-y)/(b-y) = 2/3 iff 3(3x-y)=2(4x-y) iff 9x-3y=8x-2y iff y=x, that is, iff y=gcd(a,b).





Example: a=36, b=48.


You'd have to subtract 12 (=gcd(36,48)). Indeed, 36/48=3/4, 24/36=2/3.