| The ratio of the numbers of boys and girls in a school was 5: 3. Some new boys and girls were admitted to the school, in the ratio 5: 7. At this the total number of students in the school became 1200 and the ratio of boys to girls changed to 7: 5. The number of students in the school before new admission was |
A) 700
B) 720
C) 900
D) 960
Correct Answer: D
Solution :
| Let number of boys and girls in the school before new admissions are 5x and 3x, respectively. |
| Now, let 5y and 7y boys and girls are admitted in the school. |
| \[\therefore \] \[5x+3x+5y+7y=1200\] |
| \[\Rightarrow \] \[8x+12y=1200\] ... (i) |
| Also, \[\frac{5x+5y}{3x+7y}=\frac{7}{5}\] |
| \[\Rightarrow \] \[25x+25y=21x+49y\] |
| \[\Rightarrow \] \[x=6y\] ... (ii) |
| From Eqs. (i) and (ii), we get |
| \[x=120\]and \[y=20\] |
| Hence, total number of students in school before new admissions \[=5x+3x=8x=8\times 120=960\] |
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