| In a class, there are 33 students comprising of boys and girls. In a monthly test, the average score of the class was 14.The average score of girls and boys of the class was 15 and 12, respectively. Assuming that all the students had taken the test, what is the number of girls in the class? [FCI (Assistant) Grade III 2015] |
A) 11
B) 22
C) 33
D) None of these
Correct Answer: B
Solution :
| Here, total students (n) = 33, total average [a] = 14, boys average (y) = 12 and girls average (x) = 15 |
| We known that, |
| Number of girls \[=\frac{n\,(a-y)}{(x-y)}=\frac{33\times (14-12)}{(15-12)}\] |
| \[=\frac{33\times 2}{3}=11\times 2=22\] |
| Alternate Method |
| Let number of boys be x. |
| Then, number of girls \[=33-x\] |
| Sum of marks of all students \[=33\times 14=462\] |
| Sum of marks of all boys \[=12\times x\] |
| Sum of marks of all girls \[=15\times (33-x)\] |
| According to the question, |
| \[462=12x+15\,(33-x)\] |
| \[\Rightarrow \] \[462=12x-15x+495\] |
| \[\Rightarrow \] \[-\,33=-\,3x\]\[\Rightarrow \]\[x=11\] |
| \[\therefore \] Number of girls = 22 |
You need to login to perform this action.
You will be redirected in
3 sec
