Explanation:

Let’s break this down step by step:

- SSC (Boys : Girls) = 4 : 3, PO (Boys : Girls) = 8 : 13

- BOTH exams (Boys : Girls) = 2 : 1

- PO ONLY (Boys : Girls) = 1 : 2

- Boys (SSC only) are 10 more than Girls (SSC only)

- Boys (both) = 20% of Boys (SSC only)

Let’s assign variables:

Let x = Boys (SSC only).

So, Boys (both) = 0.2x.

Girls (SSC only) = x – 10.

Girls (both) = 0.5 × Boys (both) = 0.1x (since both ratio is 2:1).

From the ratios for PO only:

Boys (PO only) : Girls (PO only) = 1 : 2

Boys (PO only) = y

Girls (PO only) = 2y

Sum Boys (SSC only) + Boys (both) + Boys (PO only)

Sum Girls (SSC only) + Girls (both) + Girls (PO only)

Using the ratios, total boys to girls in PO:

(Boys (PO only) + Boys (both)) : (Girls (PO only) + Girls (both)) = 8 : 13

So,

(y + 0.2x) : (2y + 0.1x) = 8 : 13

? 13(y + 0.2x) = 8(2y + 0.1x)

? 13y + 2.6x = 16y + 0.8x

? 2.6x - 0.8x = 16y - 13y

? 1.8x = 3y

? y = 0.6x

Boys (PO only) = y = 0.6x

Boys (SSC only) = x

So, the answer is

(0.6x / x) × 100% = 60%

- Option 1: 60% 

- The numbers add up — the ratios all check out, and the percent matches option 1.

- This means the number of boys who participated only in the PO exam is 60% of those who only did SSC.