There are some boys and girls in a room. The square of the number of girls is less than the square of the number of boys by 28. If there were two more girls, the number of boys would have been the same as that of the girls. The total number of boys and girls in the room is
(a)7
(b)10
(c)14
(d)56
Answer
Answer (as printed): C
Explanation
Let the number of boys be $x$. Then, number of girls $=(x-2)$. $x^{2}-(x-2)^{2}=28 \Leftrightarrow x^{2}-(x^{2}+4-4x)=28 \Leftrightarrow 4x-4=28 \Leftrightarrow 4x=32 \Leftrightarrow x=8$. So, number of boys = 8; number of girls = 6. Total number of boys and girls = 8 + 6 = 14.
Explanation as extracted from the printed page; notation may be imperfect.