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.