Correct Option: D

Let the two numbers are x and y.
According to the question,

x	=	5
y		7

7x = 5y
7x – 5y = 0       ...(I)

Again,	x − 40	=	17
	y − 40		27

⇒  27x – 1080 = 17y – 680
⇒  27x – 17y = 1080 – 680
⇒  27x – 17y = 400       ...(II)
From (I) × 17 – (II) × 5, we have

Putting the value of x in equation (I)
7 × 125 = 5y

∴  y =	7 × 125	= 175
	5

∴ Difference of the numbers
= 175 – 125 = 50
Second Method :
Here, a = 5, b = 7, x = 40
c = 17, d = 27
The two numbers are

=	xa(d − c)
	ad − bc

=	40 × 5(27 − 17)
	5 × 27 − 7 × 17

=	200 × 10
	135 − 119

=	2000	=	500
	16		4

1st Number = 125

And =	xb(d − c)
	ad − bc

=	40 × 7(27 − 17)
	5 × 27 − 7 × 17

=	280 × 10
	135 − 119

=	2800	=	700
	16		4

2nd Number = 175
Their difference= 175 – 125 = 50