In a 2-digit number, the ten's digit is two times its unit's digit and the number is 12 less than two times the number obtained by interchanging its digits. Find the original number.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 84
A two-digit number with tens digit a and units digit b has the value 10a + b; interchanging the digits gives 10b + a.
Let the units digit be x; the tens digit is 2x
Number \(=10(2x)+x=21x\)
Reversed number \(=10x+2x=12x\)
The number is 12 less than twice the reversed number: \(21x=2(12x)-12\)
\(21x=24x-12\), so \(3x=12\) and \(x=4\)
Number \(=21\times4=84\)