In a co-educational school there are 15 more girls than boys. If the number of girls is increased by 10\% and the number of boys is also increased by 16\%, there would be nine more girls than boys. What is the number of students in the school?
(a)125
(b)140
(c)255
(d)265
Answer
Answer (as printed): D
Explanation
Let the number of boys be $x$. Then, number of girls $=x$ +15 . $\therefore 110 \%$ of $(x+15)-116 \%$ of $x=9$ $\Rightarrow \quad \frac{110}{100}(x+15)-\frac{116}{100} x=9 \Rightarrow 110 x+1650-116 x=900$ $\Rightarrow 6 x=750 \Rightarrow x=125$. Hence, number of students in the school $$=x+(x+15)=(2 x+15)=2 \times 125+15=265 .$$
Explanation as extracted from the printed page; notation may be imperfect.