In a 2-digit number unit's digit is 5 more than the ten's digit. If 5 times the given number is 24 more than two times the number obtained by interchanging the digits of the given number, then the given number is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 38
A two-digit number with tens digit \(a\) and units digit \(b\) has the value \(10a+b\); interchanging the digits gives \(10b+a\).
Tens digit \(=a\), units digit \(=a+5\)
The number \(=10a+(a+5)=11a+5\)
Digits interchanged \(=10(a+5)+a=11a+50\)
\(5(11a+5)=2(11a+50)+24\)
\(55a+25=22a+124\), so \(33a=99\) and \(a=3\)
The number \(=11\times3+5=38\)
Shortcut: Every option has its units digit 5 more than its tens digit, so test only the second condition, 5 times the number against twice the reversed number + 24:
16: \(80\) against \(2\times61+24=146\), no
27: \(135\) against \(2\times72+24=168\), no
38: \(190\) against \(2\times83+24=190\), equal