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 1,200 and the ratio of boys to girls changed to 7: 5. What was the number of students in the school before new admissions?

Created: 3 months ago | Updated: 3 months ago

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প্রশ্নে বলা হচ্ছে যে, একটি স্কুলে বালক ও বালিকার অনুপাত 5 : 3. ঐ স্কুলে 5 : 7 অনুপাতে আরো কিছু বালক বালিকা ভর্তি হলো । এর ফলে মোট শিক্ষার্থীর পরিমাণ হলো 1,200 এবং তাদের অনুপাত হলো 7 : 5. ভর্তির পূর্বে ঐ স্কুলে মোট শিক্ষার্থীর সংখ্যা কত ছিল?

Let, at first

The number of boys was 5x and girls was 3x

∴ Total number of students = 5x + 3x = 8x

The number of boys got admitted = 5y and girls got admitted = 7y.

∴ Total new students = 5y + 7y = 12y

So, we can write 8x + 12y = 1,200

$\Rightarrow 4 (2 x + 3 y) = 1200$

$∴ 2 x + 3 y = \frac{1200}{4} = 300 . . . . . . . . (i)$

$A n d \frac{5 x + 5 y}{3 x + 7 y} = \frac{7}{5}$

$\Rightarrow 25 x + 25 y = 21 x + 49 y$

$\Rightarrow 4 x = 24 y$

$∴ x = \frac{24 y}{4} = 6 y . . . . . . . . . . (i i)$

Putting the value of x in equation (i) we get

$2 x + 3 y = 300$

$\Rightarrow (2 \times 6 y) + 3 y = 300$

$\Rightarrow 12 y + 3 y = 300$

$\Rightarrow 15 y = 300$

$∴ y = \frac{300}{15} = 20$

Putting y = 20 in equation (ii) we get
x=6y

$∴ x = 6 \times 20 = 1120$

$∴ T h e n u m b e r o f s t u d e n t, b e f o r e a d m i s s i o n w a s = 8 x = 8 \times 120 = 960 (a n s w e r) .$

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