When a number is divided by 6, it becomes 45 less than the number itself. What is the number?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 54
Dividing by 6 leaves \(\displaystyle\frac{1}{6}\) of the number, so the fall is \(\displaystyle\frac{5}{6}\) of the number.
\(\displaystyle x-\frac{x}{6}=45\)
\(\displaystyle\frac{5x}{6}=45\)
\(\displaystyle x=\frac{45\times6}{5}=54\)
Check: \(54\div6=9\) and \(54-9=45\)
The number is 54.
Why the other options are incorrect
Option (1) 270 — Incorrect. \(270\div6=45\) and \(270-45=225\), so the number is reduced by 225, not 45.
Option (3) 9 — Incorrect. \(9\div6=1.5\) and \(9-1.5=7.5\), so the number is reduced by 7.5, not 45.
Option (4) 60 — Incorrect. \(60\div6=10\) and \(60-10=50\), so the number is reduced by 50, not 45.