Question

Two towns $A$ and $B$ are $60km$ 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

• A. town $B$
• B. $45km$ from town $A$
• C. town $A$
• D. $45km$ from town $B$

Answer 1

The correct option is C

town $A$

Explanation for the correct option:

Minimum distance :

Let the school be built at $xkm$ from town $A$.

Hence, the school will be at $\left(60-x\right)km$ from town $B$.

Total distance travelled by $150$ students of town $A$$=150xkm$

Total distance travelled by $50$ students of town $B$$=50\times \left(60-x\right)$

$=\left(3000-50x\right)km$

Total distance travelled by $200$ students $=150x+3000-50x$

$=\left(100x+3000\right)km$

This distance will be minimum for $x=0$

Thus the school should be built in town $A$.

Hence option(C) is the correct answer.