A factory `D` is to be connected by a road with a straight railway line on which a town `A` is situated. The distance `D B` of the factory to the railway line is `5sqrt(3)k mdot` Length `A B` of the railway line is 20km. Freight charges on the road are twice the charges on the railway. The point `P(A P

Options

A. BP=5 km
B. AP=5 km
C. BP=7.5 km
D. none of these

Answer

1

Explanation

Let the charges for railway line be k Rs km
Now total freight charges ,`T =kx+2k sqrt((20-x)^(2)+75)`
Let `(dt)/(dx)=0`
or `k+2k(2(x-20))/(2sqrt(x-20)^(2)+75)=0`
`4(x-20)^(2)=75+(x-20)^(2)`
`(x-20)^(2)=25`
`x=25,15 or x=15 (as APltAB)
or `PB =AB-AP=20 -15 =5km