Quantitative Aptitude Ques 1016

Question: There are some boys and girls in a room. The square of the number of the girls is less than the square of the number of boys by 28. If there were 2 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 are

Options:

A) 56

B) 14

C) 10

D) 7

Show Answer

Answer:

Correct Answer: B

Solution:

  • Let the number of boys and girls in the room be x and y, respectively. According to the question, $ x^{2}-y^{2}=28 $ and $ x=y+2 $ $ x-y=2 $ Now, $ x^{2}-y^{2}=(x-y)(x+y)=2(x+y) $

$ \Rightarrow $ $ 28=2(x+y) $

$ \Rightarrow $ $ x+y=14 $

$ \therefore $ Total number of boys and girls $ =14 $

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