The digits of a 3 - digit number are in AP, and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number.

Question

Philoid · Accepted Answer

To Find: The number

Given: The digits of a 3 - digit number are in AP, and their sum is 15.

Let required digit of 3 - digit number be (a - d), (a), (a + d). Then,

(a - d) + (a) + (a + d)=15 3a = 15 a = 5

(Figure show 3 digit number original number)

5 - d

5

5 + d

(Figure show 3 digit number in reversing form)

5 + d

5

5 - d

So, (5 + d)100 + 510 + (5 - d)1 = {(5d)100 + 510 + (5 + d)1} – 594

200d – 2d = – 594 d = –3 and a = 5

So the original number is 852