Answer:
875
Step-by-step 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](https://tex.z-dn.net/?f=y%3D%202%2Bz)
Next, the hundred digit one greater than the tens digit.
∴![x= 1+y](https://tex.z-dn.net/?f=x%3D%201%2By)
The sum of the tens and the hundreds digits is three times the units digit.
∴![x+y= 3z](https://tex.z-dn.net/?f=x%2By%3D%203z)
Now, substituting the value in the equation.
![x+y= 3z](https://tex.z-dn.net/?f=x%2By%3D%203z)
⇒ ![(1+y)+y= 3\times (y-2)](https://tex.z-dn.net/?f=%281%2By%29%2By%3D%203%5Ctimes%20%28y-2%29)
solving it to get value of y
⇒ ![2y+1= 3y-6](https://tex.z-dn.net/?f=2y%2B1%3D%203y-6)
⇒![-y= -7](https://tex.z-dn.net/?f=-y%3D%20-7)
∴ ![y=7](https://tex.z-dn.net/?f=y%3D7)
Next, finding value of z
y= ![2+z](https://tex.z-dn.net/?f=2%2Bz)
substituting the value of y and subtracting both side by 2
∴ z= ![7-2= 5](https://tex.z-dn.net/?f=7-2%3D%205)
Last, finding the value of x
![x=1+y](https://tex.z-dn.net/?f=x%3D1%2By)
substituting the value of y
∴ x= 8
xyz= 875