If two numbers are in the ratio 2 : 3 and the ratio becomes

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If two numbers are in the ratio 2 : 3 and the ratio becomes 3 : 4 when 8 is added to both
the numbers, then the sum of the two numbers is

1. 10
2. 80
3. 40
4. 100

Correct Option: C

Let the numbers be 2x and 3x respectively.
According to the question,

2x + 8	=	3
3x + 8	=	4

⇒ 9x + 24 = 8x + 32
⇒ 9x – 8x = 32 – 24 = 8
⇒ x = 8
∴ Sum of numbers = 2x + 3x
= 5x
= 5 × 8 = 40
Second Method :
Here, a = 2, b = 3, x= 8, c = 3, d = 4

1st Number =	xa(c − d)
	ad − bc

=	8 × 2(3 − 4)
	2 × 4 − 3 × 3

=	−16	= 16
	−1

2nd Number =	xa(c − d)
	ad − bc

=	8 × 3(3 − 4)
	2 × 4 − 3 × 3

=	−24	= 24
	−1

Sum of numbers = 16 + 24 = 40