Explanation:

Let’s break down what’s actually happening here, piece by piece:

- There are Boys and Girls. Some do SSC, some do PO, some do both.

- For SSC, the Boy : Girl ratio is 4:3.

- For PO, the Boy : Girl ratio is 8:13.

- For BOTH PO and SSC, the Boy : Girl ratio is 2:1.

- For PO only, the Boy : Girl ratio is 1:2.

- Boys in SSC only = Girls in SSC only + 10.

- Boys who do BOTH = 20% of Boys who do SSC only.

Here’s how the variables work together:

1. Let girls in SSC only = x; so boys in SSC only = x + 10.

2. Boys in BOTH = 20% of (x + 10) = 0.2(x + 10); so girls in BOTH = (1/2) × 0.2(x +10) = 0.1(x + 10).

3. Ratio for SSC (boys to girls): [(x+10)+0.2(x+10)] : [x+0.1(x+10)] = 4 : 3.

- SSC total boys = x+10+0.2(x+10) = 1.2x+12.

- SSC total girls = x+0.1(x+10) = 1.1x+1.

- Ratio: (1.2x+12)/(1.1x+1) = 4/3 ? cross multiply and solve: 3(1.2x+12) = 4(1.1x+1) ? 3.6x+36 = 4.4x+4 ? 0.8x = 32 ? x=40.

- So, boys SSC only = 50, girls SSC only = 40.

- Boys both exams = 0.2*50 = 10; girls both = 5.

4. Build PO counts:

- Participants in only PO: Let’s call boys PO only = y, so girls PO only = 2y (since ratio is 1:2).

- Participants in both: boys = 10 (already found), girls = 5.

- Total boys in PO = y + 10.

- Total girls in PO = 2y + 5.

- Ratio for PO: (y+10):(2y+5) = 8:13.

- Cross multiply: 13(y + 10) = 8(2y + 5) ? 13y + 130 = 16y + 40 ? 3y = 90 ? y=30

- PO only: boys = 30, girls = 60.

5. Gather all numbers:

- Only SSC: boys = 50, girls = 40.

- Both: boys = 10, girls = 5.

- Only PO: boys = 30, girls = 60.

Add totals:

- Boys: 50 (SSC only) + 10 (both) + 30 (PO only) = 90.

- Girls: 40 + 5 + 60 = 105.

Total participants: 90 + 105 = 195

- So the answer is Option 4: 195—that’s the right one.

Quick check on the other options:

- 190/199/250/205 - None fit the calculations above. 195 is spot on for every ratio and relationship they listed, so you nailed it.