Two numbers are in the ratio 5 : 7. If 9 is subtracted from

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Two numbers are in the ratio 5 : 7. If 9 is subtracted from each of them, their ratio becomes 7 : 11. The difference of the numbers is

1. 6
2. 12
3. 15
4. 18

Correct Option: B

Let the numbers be 5x and 7x.

Now,	5x − 9	=	7
	7x − 9		11

⇒ 11 (5x – 9) = 7 (7x – 9)
⇒ 55x – 99 = 49x – 63
⇒ 55x – 49x = 99 – 63
⇒ 6x = 36
⇒ x = 6
∴ Required difference
= 7x – 5x = 2x = 2 × 6 = 12
Second Method :
Here, a = 5, b = 7, x = 9, c = 7, d = 11

1st Number =	xa(d − c)
	ad − bc

=	9 × 5(11 − 7)
	5 × 11 − 7 × 7

=	45 × 4
	55 − 49

=	45 × 4	= 30
	6

2nd Number =	xb(d − c)
	ad − bc

=	9 × 7(11 − 7)
	5 × 11 − 7 × 7

=	63 × 4
	55 − 49

=	63 × 4	= 42
	6