The middle digit of a number between 100 and 1000 is zero, and the sum of the other digits is 11. If the digits are...

      

The middle digit of a number between 100 and 1000 is zero, and the sum of the other digits is 11. If the digits are reversed the number so formed exceeds the original by 495. Find the number.

  

Answers


Kavungya
Let x be the digit in the hundreds place and y be the digit in the units place, since the digit in the tens place is 0, then the total value of the number is:
100x + y
If the digits are reversed then total value of the number is:
100y + x
100y + x – (100 x + y) = 495
Difference then is: 99y – 99y = 495
y – x = 5 …………………….(i)
Sum of the other two digits
x + y = 11 ……………………….(ii)
From (i) and (ii) we find x = 3 and y = 8 hence the number is 308
Kavungya answered the question on September 24, 2019 at 12:21


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