Two numbers are in the ratio 7 : 11. If 7 is added to each

Two numbers are in the ratio 7 : 11. If 7 is added to each of the numbers, the ratio becomes
2 : 3. The smaller number is

Let the numbers be 7x and 11x respectively.

∴	7x + 7	=	2
	11x + 7		3

∴ 22x + 14 = 21x + 21
⇒ x = 7
∴ Smaller number
= 7x = 7 × 7 = 49
Second Method :
Here, a = 7, b = 11, x = 7, c= 2, d = 3

1st Number=	xa(c − d)
	ad − bc

=	7 × 7(2 − 3)
	7 × 3 − 11 × 2

=	49 × −1	= 49
	21 − 22

2nd Number =	xb(c − d)
	ad − bc

=	7 × 11(2 − 3)
	7 × 3 − 11 × 2

=	77 × −1	= 77
	21 − 22

∴ Smallest number = 49