55% of all teachers in a school are females. If 8% of the female teachers in that school teach 5 classes a day, what is the number of female teachers who do not teach 5 classes a day? (N.I.F.T., 2007) I. There are 135 male teachers in the school. II. There are 27 male teachers in the school who do not teach 5 classes a day.
Answer
SELF-PRACTICE — the source book printed no answer.
Nothing is invented here, so this question has no answer on record.
Explanation
Let the total number of teachers in the school be $x$. From I, we have $$(100-55) \% \text { of } x=135 \Rightarrow x=\frac{135 \times 100}{45}=300 .$$ ∴ Reqd. number of teachers = (100-8)\% of 55\% of $$300=\left(\frac{92}{100} \times \frac{55}{100} \times 300\right) .$$ So, I alone gives the answer while II alone is insufficient. $$\text { ∴ Correct answer is }(a) \text {. }$$
Explanation as extracted from the printed page; notation may be imperfect.