Question

a va b zalda bir necha o‘quvchi bor edi. agar a zaldan b zalga 14 nafar o‘quvchi o‘tsa, ikkala zaldagi o‘quvchilar soni teng bo‘ladi. agar b zaldan a zalga 4 nafar o‘quvchi o‘tsa, a zaldagi o‘quvchilar sonining b zaldagi o‘quvchilar soniga nisbati 8 : 5 bo‘ladi. b zalda necha nafar o‘quvchi bor?

Explanation:

Step1: Define variables

Let the number of students in A be \( x \) and in B be \( y \).

Step2: From first condition

If 14 students move from A to B, they are equal: \( x - 14 = y + 14 \)
Simplify: \( x = y + 28 \)

Step3: From second condition

If 4 students move from B to A, ratio \( A:B = 8:5 \):
\( \frac{x + 4}{y - 4} = \frac{8}{5} \)

Step4: Substitute \( x \)

Substitute \( x = y + 28 \) into the ratio equation:
\( \frac{(y + 28) + 4}{y - 4} = \frac{8}{5} \)
Simplify numerator: \( \frac{y + 32}{y - 4} = \frac{8}{5} \)

Step5: Cross - multiply

\( 5(y + 32) = 8(y - 4) \)
Expand: \( 5y + 160 = 8y - 32 \)

Step6: Solve for \( y \)

Subtract \( 5y \): \( 160 = 3y - 32 \)
Add 32: \( 192 = 3y \)
Divide by 3: \( y = 64 \)

Answer:

64