A survey of $600$ schools in India was conducted to gather information about their online teaching learning processes $\text{(OTLP)}$. The following four facilities were studied.
$\text{F1}:$ Own software for $\text{OTLP}$
$\text{F2}:$ Trained teachers for $\text{OTLP}$
$\text{F3}:$ Training materials for $\text{OTLP}$
$\text{F4}:$ All students having Laptops
The following observations were summarized from the survey.
- $80$ schools did not have any of the four facilities$ – \text{F1, F2, F3, F4}. $
- $40$ schools had all four facilities.
- The number of schools with only $\text{F1},$ only $\text{F2},$ only $\text{F3},$ and only $\text{F4}$ was $25,30,26$ and $20$ respectively.
- The number of schools with exactly three of the facilities was the same irrespective of which three were considered.
- $313$ schools had $\text{F2}.$
- $26$ schools had only $\text{F2}$ and $\text{F3} \; (\text{but neither F1 nor F4}).$
- Among the schools having $\text{F4}, 24$ had only $\text{F3},$ and $45$ had only $\text{F2}.$
- $162$ schools had both $\text{F1}$ and $\text{F2}.$
- The number of schools having $\text{F1}$ was the same as the number of schools having $\text{F4}.$
What was the number of schools having facilities $\text{F2}$ and $\text{F4}$
- $185$
- $45$
- $95$
- $85$