Question

Six–elevenths of a first number equals twenty-two percent of a second number. The second number equals one-fourth of a third number. If the third number is \(2400\), then what is \(45%\) of the first number?

• A. \(111.7\)
• B. \(117.6\)
• C. \(123.4\)
• D. None of these

Hint:

Percent relations often simplify nicely when converted to fractions. Link the numbers step-by-step, then compute the required percentage at the end.

Answer 1

The Correct Option is D

Solution:
Step 1 (Translate relations into equations).
Let the first, second and third numbers be \(A,B,C\). \[ \frac{6}{11}A = 22% \text{ of } B = \frac{11}{50}B \quad\quad A = \frac{11}{50}\cdot\frac{11}{6}B=\frac{121}{300}B. \] Step 2 (Use the link to the third number).
Given \(B=\frac{1}{4}C\) and \(C=2400 B=600\). Step 3 (Find the first number).
\[ A=\frac{121}{300}\times 600=242. \] Step 4 (Compute \(45%\) of the first number).
\[ 0.45\times 242=\frac{45}{100}\times 242=\frac{9}{20}\times 242=\frac{2178}{20}=108.9. \] This value is not among (a)–(c), so the correct choice is “None of these”. \[ {108.9 \ \text{(Option d: None of these)}} \]