Problema Solution

the digits of 3 digit natural number are in A.P and their sum is 18.The number obtained by reversing digits is 594 less than original number,find the original number. (hint:(a+d)at unit's place, 'a ' at 10th place, & (a-d) at 100th place).

Answer provided by our tutors

let the number be 'x' and the digits be


(a-d) at unit's place,

a at 10th place, &

(a+d) at 100th place


this is true since we know that their are in A.P.


then we can write for the number


x = (a-d) + 10*a + 100*(a + d)


the sum of the digits is 18


a + d + a + a - d = 18


3*a = 18


a = 6


the number obtained by reversing digits is: a + d + 10*a + 100*(a - d) = 111*a - 99*d is 594 less than original number


(a - d) + 10*a + 100*(a + d) - 594 = a + d + 10*a + 100*(a - d)


111*a + 99*d - 594 = 111*a - 99*d


198*d = 594


d = 3


so the original number has digits: 3, 6, 9 thus the number is 963


indeed


3 + 6 + 9 =19


963 = 594 + 369


the original number is 936.