Two towns A and $5$ are $60$ km apart. A school is to be built to serve $150$ students in town A and $50$ students in town B. If the total distance to be travelled by all $200$ students is to be as small as possible, then the school should be built at

Let the school at a distance $x$ km from town A. Then the distance of school from town B is $(60-x)$ km. 

Distance travelled by $150$ students of town A $= 150x$

Distance travelled by $50$ students of town B $= 50(60-x)$

Distance travelled by $200$ students, $D=150x+3000-50x$

$D=f\left(x\right)=100x+3000$

$D$ is least when $x=0$

Hence school should be build at town A.