Question

The digit of a positive number of three digits are in A.P. and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number

Answer 1

Sol: Let the digit at the hundredth place of the number be (a + d). 

Digit at the tens place be a. 

Digit at the ones place be (a – d). 

Sum of the digits = 15 (a + d) + a + (a – d) = 15 3a = 15 ⇒ a = 5

The number formed by the digits = 100 (5 + d) + 10 (5) + (5 – d) = 555 + 99d 

The number formed by reversing the digits = 100 (5 - d) + 10 (5) + (5 + d) = 555 – 99d 

Given that the number formed by reversing the digits is 594 less the original number.

⇒ (555 + 99d) – (555 - 99d) = 594

⇒ 198 d = 594

⇒ d = 3

(a + d) = (5 + 3) = 8, a = 5, (a – d) = (5 – 3) = 2. 

Hence, the number formed by the digits = 100(8) + 10(5) + 1(2) = 852.