The ratio between two numbers is 3 : 4. If each number is

The ratio between two numbers is 3 : 4. If each number is increased by 6, the ratio becomes 4 : 5. The difference between the numbers is

Let the numbers be 3x and 4x.

∴	3x + 6	=	4
	4x + 6		5

⇒ 16x + 24 = 15x + 30
⇒ x = 30 – 24 = 6
∴ Required difference = 6
Second Method :
Here, a = 3, b= 4, x = 6
c = 4, d = 5

The numbers are =	xa(c − d)
	ad − bc

=	6.3(4 − 5)
	3 × 5 − 4 × 4

=	18 × −1	= 18
	15 − 16

=	xb(c − d)
	ad − bc

=	6 × 4(4 − 5)
	3 × 5 − 4 × 4

=	24 × (− 1)	= 24
	15 − 16

Numbers are 24 and 18.
Their difference = 24 – 18 = 6