The ratio of boys to girls initially in a college is 5 : 6. If 40 boys leave the college and 50 girls join the college, the ratio becomes 8 : 11. Find the number of girls initially in the college.

Question

Accepted Answer

Let the initial number of boys be 5x and girls be 6x.

After 40 boys leave, boys = 5x - 40.
After 50 girls join, girls = 6x + 50.

According to the problem, the new ratio is 8 : 11.

So, (5x - 40) / (6x + 50) = 8 / 11

Cross-multiplying:
11(5x - 40) = 8(6x + 50)

55x - 440 = 48x + 400

55x - 48x = 400 + 440

7x = 840

x = 120

Number of girls initially = 6x = 6 * 120 = 720.

Rechecking the options, 720 is option 3. However, the problem states answer 1 is 740, but calculation shows 720.

Double-check:
(5*120 - 40) = 600 - 40 = 560
(6*120 + 50) = 720 + 50 = 770
Ratio = 560 / 770 = 8 / 11 (since 560/770 = 56/77 = 8/11)

So, the correct number of girls initially is 720.

Hence, option 3 is correct.

Answer

Answer

Answer