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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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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
1). 700
2). 720
3). 900
4). 960

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2 answers

0 vote
Answered by on | Votes 0 |
Its tough but option 4 seems correct

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2 vote
Answered by on | Votes 2 |

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.
$\therefore$ 5x + 3x + 5y + 7y = 1200
=> 2x + 3y = 300 ............(i)

and, $\frac{5x+5}{3x+7y}$ = $\frac{7}{5}$

=> 25x + 25y = 21x + 49y
=> 4x = 24y
=> x = 6y ......... (ii)
From equation (i),
4x + 6y = 600
=> 5x = 600

=> x = 120
$\therefore$ Original number of students= 8x = 960




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