Option 4 : 8

Given:

x is subtracted from,

20, 28, 29 and 40

Concept Used:

If a, b, c, and d are in proportion,

then a/b = c/d

If y is mean proportion of x, y, and z,

then y2 = x × z

Calculation:

⇒ (20 + x)/(28 + x) = (29 + x)/(40 + x)

⇒ (20 + x)(40 + x) = (29 + x)(28 + x)

⇒ 800 + 20x + 40x + x2 = 812 + 29x + 28x + x2

⇒ 800 + 60x = 812 + 57x

⇒ 812 – 800 = – 57x + 60x

⇒ 12 = 3x

⇒ x = 12/3

⇒ x = 4

The two numbers are,

3x + 4

⇒ 3(4) + 4

⇒ 16

2x – 4

⇒ 2(4) – 4

⇒ 4

Now mean proportion of 16 and 4,

⇒ √(16 × 4)

⇒ √64

⇒ 8

∴ The mean proportion of 5x+1 and 7x + 3 is 8.