Question

Two towns A and B 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 200 students is to be small as possible, then the school should be built at

• A. town B
• B. 45 Km from town A
• C. town A
• D. 45 Km from town B

Answer 1

Answer: (C)

town A

Let the school be at a distance x km from the town A.
Then the distance of school from town $B=(60-x)$km
Distance travelled by 150 students of town $A=150x$
Distance travelled by 50 students of town $B=50(60-x)$
So, total distance travelled by 200 students $D=150x+3000-50x$
$D=f\left(x\right)=100x+3000$
Clearly D is least when $x=0$
Hence, the school should be built at town A.