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 all 200 students is to be as 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 :
town $$A$$
Solution :
Let the distance of school from $$A$$ = $$x$$
∴ The distance of the school form $$B$$ = $$60 - x$$
Total distance covered by 200 students
$$= 2[150 x +50(60 - x)] = 2[100 x + 3000]$$
This is min., when $$x$$ = 0
∴ school should be built at town $$A.$$
Releted MCQ Question on Algebra >> Quadratic Equation
Releted Question 1
If $$\ell ,m,n$$ are real, $$\ell \ne m,$$ then the roots by the equation: $$\left( {\ell - m} \right){x^2} - 5\left( {\ell + m} \right)x - 2\left( {\ell - m} \right) = 0$$ are