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Question
The sum of digits of a two digit number is 10. If the new number formed by reversing the digits is less than the original number by 36. Then find the original number.
The sum of digits of a two digit number is 10. If the new number formed by reversing the digits is less than the original number by 36. Then find the original number.
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Solution
The correct option is B 73
Let the unit place digit be x
Ten's place digit =10−x
Original number = 10×(10−x)+x
=100−10x+x
=100−9x
Reversing the digit:
Unit digit =10−x
Ten's digit =x
New number formed = 10×x+10−x
=9x+10
As new number is less than the original number by 36
New number = original number −36
9x+10=100−9x−36
18x=100−10−36
18x=54
x=3
Original number =100−9x
=100−9×3
=100−27
=73
Original number =73.
So, option C is correct.
Let the unit place digit be x
Ten's place digit =10−x
Original number = 10×(10−x)+x
=100−10x+x
=100−9x
Reversing the digit:
Unit digit =10−x
Ten's digit =x
New number formed = 10×x+10−x
=9x+10
As new number is less than the original number by 36
New number = original number −36
9x+10=100−9x−36
18x=100−10−36
18x=54
x=3
Original number =100−9x
=100−9×3
=100−27
=73
Original number =73.
So, option C is correct.
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