In a certain organisation, 40\% employees are matriculates, 50\% of the remaining are graduates and the remaining 180 are post-graduates. What is the number of graduate employees?
(a)180
(b)240
(c)300
(d)360
Answer
Answer (as printed): A
Explanation
Let the total number of employees be $x$. Then, $(100-50) \%$ of $(100-40) \%$ of $x=180 \Rightarrow 50 \%$ of 60\% of $x=180$ $$\Rightarrow\left(\frac{50}{100} \times \frac{60}{100} \times x\right)=180 \Rightarrow x=\left(\frac{180 \times 10}{3}\right)=600 .$$ ∴ Number of graduate employees $=50 \%$ of 60\% of $x$ $$=\left(\frac{50}{100} \times \frac{60}{100} \times 600\right)=180 .$$
Explanation as extracted from the printed page; notation may be imperfect.