Question

A three-digit number has tens digit two greater than the units digit and the hundreds digit one greater than the tens digit. The sum of the tens and the hundreds digits is three times the units digit. What is the number?

Answer 1

875

Explanation:

As given, there is a three digit number

So, let assume three digit number be `xyz`.

Now, as given tens digit is 2 greater than the unit digit.

∴
`y= 2+z`

Next, the hundred digit one greater than the tens digit.

∴
`x= 1+y`

The sum of the tens and the hundreds digits is three times the units digit.

∴
`x+y= 3z`

Now, substituting the value in the equation.

`x+y= 3z`

⇒
`(1+y)+y= 3* (y-2)`

solving it to get value of y

⇒
`2y+1= 3y-6`

⇒
`-y= -7`

∴
`y=7`

Next, finding value of z

y=
`2+z`

substituting the value of y and subtracting both side by 2

∴ z=
`7-2= 5`

Last, finding the value of x

`x=1+y`

substituting the value of y

∴ x= 8

xyz= 875