Question

A number is formed by three consecutive digits. If the digits are reversed
the difference of the numbers is 33 times the greatest digit. Find the number​

Answer 1

Let : Three consecutive Number be

• x
• x+1
• x+2

let Three digit number be , 100(x+2) + 10(x+1) + x

Given :

difference between 3digit number & number formed by reversing digit = 33(greatest number)

To find : Three digit number

Solution :

number is 100(x+2) + 10(x+1) + x

Number obtained by reversing = 100x + 10(x+1) + (x+2)

According to question,

=> 100(x+2) + 10(x+1) + x - { 100x + 10(x+1) + (x+2) } = 33(x+2)

=> 100x + 200 + 10x + 10 + x - 100x - 10x- 10 -x - 2 = 33x + 66

=> 200 - 2 = 33x + 66

=> 198 - 66 = 33x

=> 33x = 132

=> x = 132/33

=> x = 4

therefore

x+1 = 4+1 = 5

x+2 = 4+2 = 6

therefore number = 100(x+2) + 10(x+1) + x

=> 100(6) + 10(5) + 4

=> 654

ANSWER : Required 3 digit number = 654