Question

State government of Uttrakhand has to sign a project to set up sign boards along the road of a hill station .The cost per sign board is $Rs.1100$ and increases by $Rs.100$ as we move up to set the next sign board . What is the total cost of the project for setting sign boards along a $20KM.$ long road , if distance between subsequent sign boards is $\frac{1}{2}KM$

• A. $Rs.142000$
• B. $Rs.132000$
• C. $Rs.122000$
• D. $Rs.152000$

Answer 1

The correct option is B $Rs.132000$

The cost of sign boards forms an A.P. with a common difference of $100$
Total number of sign boards $=n=\frac{20}{\frac{1}{2}}=40$
$1100,1200,1300,\mathrm{1400......}$
$S=1100+1200+1300+\mathrm{1400.......}$
$S=\frac{n}{2}\{2a+(n-1\left)d\right\}S=\frac{40}{2}\left\{2\right(1100)+(40-1\left)100\right\}S=20(2200+3900)=20\left(6100\right)=122000$
So total cost is $Rs.122000$
Option $B$ is correct