Sum of the digits of a two digit number is 7. The difference between
original number and the number obtained by reversing the digits is
27. Find the original number.
Answers
2x-10+(-10+2x) = 7
2x+2x-10+10 =7
4x
The original number is 52
Solution:
Given that sum of the digits of a two digit number is 7
Let the unit digit of original number be "a"
Then the tens digit is "7 - a"
The number formed by these digits = 10 x tens digit + units digit
The original number = 10(7 - a) + a = 70 - 9a
On reversing the digits, we obtain
tens digit = a
Units digit = 7 - a
The number obtained on reversing the digits = 10a + 7 - a = 9a + 7
Given that, difference between original number and the number obtained by reversing the digits is 27
Hence we get,
70 - 9a - (9a + 7) = 27
70 - 9a - 9a - 7 = 27
63 - 18a = 27
18a = 63 - 27
a = 2
Thus the original number has tens digit = 7 - a = 7 - 2 = 5
The original number has units digit = a = 2
Therefore the two digit original number is 52
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