Explanation:

Let’s break it down, point by point:

- There are 750 girls in total.

- The ratio of girls in A : B : C is 6:10:9. So, A = 180, B = 300, C = 270.

- 80 girls play all three games (AnBnC = 80).

- Only B has 60 girls (B only = 60).

- Only A is 30 more than only C (Let's call Only C = x, then Only A = x + 30).

- (A + C) only = 15 girls. It’s 50 less than Only A ? Only A = 65, so Only C = 35.

- (B + C) only is 125 more than (A + C) only ? (B + C) only = 140.

- Using all these, tally the participants for only groups and overlaps.

Calculating only A and (A+B) only:

- Only A = 65

- (A+B) only: A's total - (only A) - (A+B+C) - (A+C only)

- But more directly, from set equations and subtracting all other knowns from B:

- B = 300 = (only B) + (A+B only) + (B+C only) + (A+B+C)

- 300 = 60 + (A+B only) + 140 + 80

- 300 = 280 + (A+B only) ? (A+B only) = 20

The ratio of Only A : (A+B) only = 65 : 20 = 13 : 4

So, your answer is option 4, 13 : 4.

Here’s what the options mean:

- Option 1: 14:5 (Not matching)

- Option 2: 13:5 (Nope)

- Option 3: 15:7 (Nope)

- Option 4: 13:4 (Matches)

- Option 5: 12:13 (Nope)

Hope that clears it up—your calculations are solid!