Question

20 students out of 75 play only football 20% of the remaining play only cricket than 25% of the remaining play both football and cricket how many play Both cricket and football

Answer 1

Answer:

11 students.

Step-by-step explanation:

$\text{Total no. of students = 75}\\\\\text{No. of students playing only football = 20}\\\\\text{Remaining students = 75 - 20 = 55}\\\\\text{Percentage of students playing only cricket in the remaining ones = 20} \%\\\\\text{Thus, No. of students playing only cricket in the remaining ones}\\\\= 20 \% \: of \: 55\\\\= \dfrac{20}{100} \times 55\\\\= \dfrac{55}{5}\\\\= \boxed{11}\\\\\text{Remaining students after removing children who play only football or only cricket}\\\\ = 55 - 11 = 44$

$\text{Now, percentage of children playing both football and cricket out of the remaining ones}\\\\= 25 \%\\\\\text{Thus, No. of children playing both football and cricket out of the remaining ones}\\\\= 25 \% \: of \: 44\\\\= \dfrac{25}{100} \times 44\\\\= \dfrac{44}{4}\\\\= \boxed{11}$

Hope it helps.