Question

The middle digit of a number between 100 and 1000 is 0, and the sum of the other digit is 11. If the digits are reversed the number so formed exceed the original number by 495. Find the original number.
A) 405
B) 408
C) 308
D) 309

Answer 1

Hint: Place the given digits it’s over, tenth and hundredth accordingly and then four equation. The first digit after the decimal represents the tenths place. The next digit after the decimal represents the hundredths place. The remaining digits continue to fill in the place values until there are no digits left.

Complete step by step solution: Let x be the digit in the units place and be the digit in the hundreds of places.
Then, since the digits are Tunis places is 0, the number will be represented by $100y+x.$
If the digits are severed the numbers so formed will be represented by $100x+y.$
Therefore:
$100x+y-\left( 100+x \right)=495$
Or $100x+y-100y-x=495$
Or $99x-99y=495$
Or $x-y=5$ ①
Now since the sum of the other digits is 11, and the middle one is 0, we have.
$x+y=11$ ②
From ① and ②, we get.
$\left( x-y \right)+\left( x+y \right)=5+11$
Or, $2x=16$
Or, $x=8.$
Putting value of \[x\ \text{in}\ \ \text{eq}\]①
$
  \text{so,} \;x-y=5 \\
 \&, \;8-y=5 \\
 \&, \;8-5=y\ \Rightarrow y=3. \\
$
Hence the numbers is 308.

Therefore the answer is C option.

Note: In this type of question, place the digits according to place asked its question and then follow the techniques. Depending upon the position of a digit in a number, it has a value called its place value. For example, the place value of the digit 6 in the number 1673 is 600 as 6 is in the hundreds place. However, if we interchange the digits 6 and 7 in the number 1673, we get a new number 1763. In 1763 the place value of the digit 6 is 60 as it is in the tens place.