The ratio of a two-digit number to the sum of its digits is 4 : 1. If the digit in the units place is 3 more than the digit in the tens place, what is the number?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 36
A two-digit number with tens digit \(a\) and units digit \(b\) has the value \(10a+b\); the two conditions give two equations in \(a\) and \(b\).
Units digit \(b=a+3\)
\(10a+b=4(a+b)\), so \(6a=3b\), that is \(b=2a\)
\(2a=a+3\), so \(a=3\) and \(b=6\)
Check: \(36\div(3+6)=4\). The number is 36.
Why the other options are incorrect
Option (1) 24 — Incorrect. \(24\div6=4\), but its units digit is only 2 more than the tens digit.
Option (2) 63 — Incorrect. Its units digit is smaller than the tens digit, and \(63\div9=7\).
Option (4) None of these — Incorrect. 36 satisfies both conditions and is among the options.