Q 28 The difference between a three digit number and the number formed by reversing its first two digits is 450. If the sum of its digits is 10, determine the number.
Ops: A.
424
В.
523
C.
613
D.
0 145
Answers
Answer:
Since after subtracting two three digit numbers we are getting a two digit number so we can operate considering two digit numbers only.
Let the two digit number be 10x+y and after reversing it will be 10y+x.
Acc to question, (10x+y) - (10y-x) = 27.
- i.e. 9x - 9y = 27.
- or, x - y = 3.
- or, x = (y+3)
Now, it is also given that sum of the digits is 12.
- i.e. x + y + 3rd digit = 12.
- or, y+3 + y + 3rd digit = 12.
- or, 3rd digit = 9 - 2y.
"y" must be less than 5.
Let's say "y" is 4 then 3rd digit = 9 - 8 = 1.
and x will be 7. i.e. 174 and after reversing we get: 147.
174 - 147 = 27.
Also considering "y" is 3 then 3rd digit = 9 - 6 = 3.
and x will be 6 i.e. 363 and after reversing we get: 336.
363 - 336 = 27.
Also considering "y" is 2 then 3rd digit = 9 - 4 = 5.
and x will be 4 i.e. 542 and after reversing we get: 524.
542 - 524 = 18. thus condition doesn't satisfies.
Therefore, the numbers can be either 174 or 363. [Ans]