When 328 is subtracted from a number, the result is \(11\frac{1}{9}\%\) of the number. Find the number.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 369
\(11\frac{1}{9}\%\) is the fraction \(\frac{1}{9}\). If what is left is \(\frac{1}{9}\) of the number, then the 328 taken away is the other \(\frac{8}{9}\).
\(\displaystyle 11\frac{1}{9}\%=\frac{100}{9}\times\frac{1}{100}=\frac{1}{9}\)
\(\displaystyle x-328=\frac{x}{9}\), so \(\displaystyle \frac{8x}{9}=328\)
\(\displaystyle x=\frac{328\times9}{8}=369\)
The number is 369.