Question

The middle digit of a number between 100 and 1000 is zero and the sum of the other digit is 13. If the digits are reversed, the number so formed exceeds the original number by 495. Find the number

Answer 1

Let the unit digit be and the 100 is digit be X.

The number is X0Y (100x + y)

By the given first condition

x + y = 13 ...(1)

If the digits are reversed the number is 100y + x.

By the given second condition.

100y + x = 100x + y + 495

−99x + 99y = 495

−x + y = 5 ...(2)

x + y = 13  ...(1)

Add (1) and (2)

2y = 18

y = 9

Substitute the value of y = 9 in (1)

x + 9 = 13

x = 13 – 9

x = 4

∴ The number is 409