A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The unit digit of the number is:

Question: A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The unit digit of the number is:

Solution:
Let the digits be x, y, z

x + y + z = 10
y = x + z

y + y = 10
⇒ y = 5

So, x + z = 5

Now,
(100z + 10y + x) - (100x + 10y + z) = 99
⇒ 99z - 99x = 99
⇒ z - x = 1

x + z + z - x = 5 + 1
⇒ 2z = 6
∴ z = 3

∴ x = 5 - 3 = 2

The number is = 253

Hence, The unit digit of the number is: 3