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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 admissions was
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- 700
- 720
- 900
- 960
Correct Option: D
Let the original number of boys and girls be 5x and 3x respectively and that of new boys and girls be 5y and 7y respectively.
∴ 5x + 3x + 5y + 7y = 1200
⇒ 2x + 3y = 300 ............(i)
| and, | = | ||
| 3x + 7y | 5 |
⇒ 25x + 25y = 21x + 49y
⇒ 4x = 24y
⇒ x = 6y ......... (ii)
4x + 6y = 600
⇒ 5x = 600 ⇒ x = 120
∴ Original number of students
= 8x = 960
