Explanation:

Let’s break this down step by step:

- First, find the number of boys in each institution (since only average and girls are given):

    Total students in A = 110*2 = 220 ? Boys in A = 220 - 80 = 140

    B: 140*2 = 280 ? Boys in B = 280 - 90 = 190

    C: 80*2 = 160 ? Boys in C = 160 - 60 = 100

    D: 96*2 = 192 ? Boys in D = 192 - 60 = 132

    E: 48*2 = 96 ? Boys in E = 96 - 40 = 56

- Now, look at what the problem says about absentees:

    In D, 3/11th of boys are absent: (3/11) * 132 = 36

    In F, 25% of the boys are absent: That’s (1/4)*F = x

- The question says: The average boys absent (from D and F) is 42.

    So, \( \frac{36 + x}{2} = 42 \)

    ? 36 + x = 84

    ? x = 48

- But x is also one-fourth of the boys in F. So,

    \( \frac{1}{4} × \text{F} = 48 \)

    ? F = 48 × 4 = 192

So, the correct answer is Option 5: 192. 

- Option 1: 176 (no math supports this)

- Option 2: 216 (off by what you’d get multiplying 48 by 4.5)

- Option 3: 168 (same issue; wouldn’t match the logic)

- Option 4: 172 (no step points to this)

- Option 5: 192    That's the number that fits the whole scenario.