The sum of the two digits of a 2-digit number is 10. If 36 is added to the number, the digits are reversed. What is the number?
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The sum of the two digits of a 2-digit number is 10. If 36 is added to the number, the digits are reversed. What is the number?
please solve the question fast
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Answer:
Let the number be xy = 10*x + y
Given x + y = 10 (i)
and
10*x + y + 36 = 10*y + x (digits of original number reversed by adding 36)
9*x - 9*y = -36
x - y = -4 (ii) dividing throughout by 9.
Adding (i) and (ii):
x + y = 10
+(x - y = -4)
We get:
2*x = 6
or x= 3
Substituting for x in (i),
3 + y = 10
or y = 10 - 3 = 7
Therefore, the original number, xy (=10*x + y) = 30 + 7 = 37.
Check: 37 + 36 = 73.