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 |
A) 56
B) 14
C) 10
D) 7
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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