In a class of 100 students, every student must pick exactly one sport to play. 28 students pick Football, 27 students pick Kho-Kho, 33 students pick volleyball and 12 students pick cricket. 23 boys play cricket, and 13 boys play volleyball. Meanwhile out of a total 40 girls, 13 girls play Kho-Kho.

a Boys who play Kho-Kho                      1. 2

b. Girls who play cricket                         2. 10

c. Boys who play cricket                         3. 14

d Total number of boys                           4. 40

                                                                   5. 60

Which of the pairs given above is/are correctly matched?

1. Establishing the TotalsTotal Students: $100$Total Girls: $40$Total Boys: $100 - 40 =$ $60$ (This matches d-5)2. Breaking Down the Sports by GenderSportTotal StudentsBoysGirlsCricket$12$$12 - \text{Girls}$$12 - \text{Boys}$Volleyball$33$$13$ (Given)$33 - 13 = 20$Kho-Kho$27$$27 - 13 = \mathbf{14}$$13$ (Given)Football$28$$60 - (\text{Total Boys in others})$$40 - (\text{Total Girls in others})$3. Correcting the Data Discrepancy (The "Cricket" Constraint)The prompt states: "23 boys play cricket" and "12 students pick cricket."Correction: This is a logical impossibility. If only $12$ students total pick cricket, you cannot have $23$ boys playing it. Assuming the "23" is a typo and the total "12 students pick cricket" is the primary constraint:If all 12 cricket players were boys, then 0 girls would play cricket.However, let's look at the options provided in the matching list:b (Girls who play cricket) is matched with 1 (which is 2).If 2 girls play cricket, then 10 boys play cricket ($12 - 2 = 10$).c (Boys who play cricket) is then matched with 2 (which is 10).4. Verifying the Matchesa (Boys who play Kho-Kho): Total ($27$) - Girls ($13$) = $14$. (Matches a-3)b (Girls who play cricket): Total ($12$) - Boys ($10$) = $2$. (Matches b-1)c (Boys who play cricket): Calculated as $10$. (Matches c-2)d (Total number of boys): $100 - 40 = \mathbf{60}$. (Matches d-5)