Two numbers are such that the ratio between them is 4 :

Two numbers are such that the ratio between them is 4 : 7. If each is increased by 4, the ratio becomes 3 : 5. The larger number is

Let the numbers be 4x and 7x.

∴	4x + 4	=	3
	7x + 4		5

⇒ 21x + 12 = 20x + 20
⇒ 21x – 20x = 20 – 12
⇒ x = 8
∴ Larger number
= 7x = 7 × 8 = 56
Second Method :
a = 4, b = 7, c = 3, d = 5, x = 4

Larger number =	xa(c − d)
	ad − bc

=	4 × 7(3 − 5)
	4 × 5 − 3 × 7

=	4 × 7 × (−2)	= 56
	20 − 21