The sum of three digits in a number is 17, the sum of square of the digits is 109. If we subtract 495 from the number, the number is reversed. Find the number.

A 863

B 953

C 872

D 854

E 683

Correct Answer: Option A

Let the number is XYZ

Let the unit Digit of the No. be Z

Let the Tens Digit of the No. be Y

Let the Hundreds Digit of The No. be X

Sum of numbers is 17 ⇒ X + Y + Z = 17 …… (Eq.1)

Sum of squares of digits is 109 ⇒ X² + Y² + Z² = 109 …….. (Eq.2)

⇒ 100X + 10Y + Z – 495 = 100Z + 10Y + X

⇒ 99X – 99Z = 495

⇒ X – Z = 5

Since number is positive all possible combinations of X and Z are (6, 1), (7, 2), (8, 3), (9, 4)

Of these four combinations only (8, 3) gives acceptable solution for Y using Eq.1 and Eq.2

⇒ Y = 6

The number is 863