Number System-Railway Maths Part VII

Square root of 18769 = 137
137 consists of 3 digits.

First multiple of 6 = 6
And 12th multiple of 6 = 72
Sum of 1st 12 multiple of 6
= 6 × (1 + 2 + .............. + 12)

Let the numbers are x and y
A/Q, x + y = 20 ——— (i)
And x²− y²= 80 ——— (ii)
Put x = 20 − y  in equation (ii)
 (20 − y)²− y² = 80
 ⇒ 400 + y² − 40y − y² = 80
 ⇒ 40y = 320 ⇒ y = 8
And x = 20 − 8 =12

Let, number = 10x + y
x + y = 8 .....(1)
10x + y + 36 = 10y + x
9(x - y) = -36 ⇒ x - y = -4 .....(2)
From (1) and (2), we get
x = 2, y = 6, Number = 26

Here, x is an even number.
Let, numbers are = x, (x + 2), (x + 4), (x + 6), (x + 8)
A/Q, x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 660,
5x + 20 = 660 ⇒ x = 128
Therefore, the number will be – 128, 130, 132, 134 and 136
Greatest number = 136 and smallest number = 128

115 + x = 100/x
15x + x² = 100 ⇒ x² + 15x = 100
Then, we get +ve root (x) = 5

Let, r = 16
then,
r²/16 = (16 × 16)/16 = 16

The difference between the biggest and the smallest fraction
= 5/6 − 2/3 = 1/6