The sum of the digit of a two digit number is 6. If the number formed by reversing the digit is less than the original number by 36. Find the number.
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Step-by-step explanation:
The number is 62.
A two digit number is 36 less than the number formed by reversing the digit.
Allowing the tens digit to be a and the units digit to be b :
10b+a=10a+b−36
⟶10b+a−a−b=10a+b−36−a−b
⟶9b9=9a−369
b=a−4
If the sum of the digit is 8, what is the number?
a+b=8
⟶a+(a−4)=8
⟶2a−4+4=8+4
⟶2a2=122
⟶a=6
The tens digit is a , so the tens digit is 6.
b=a−4
⟶b=(6)−4
⟶b=2
The units digit is b, so the units digit is 2.
Proof:
6+2=8
26=62−36
Thus the original number is 62.
Q.E.D.
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