Question

A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs. $200$ for the first day, Rs. $250$ for the second day, Rs. $300$ for the third day, etc., the penalty for each succeeding day being Rs. $50$ more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by $30$ days.

Answer 1

It can be observed that these penalties are in an A.P. having first term as $200$ and common difference as $50$.

$a=200,d=50$

$Sumuptonterms$ $\left(S_n\right)=\frac{n}{2}[2a+(n-1\left)d\right]$

Penalty that has to be paid if he has delayed the work by $30$ days

$=S_{30}$
$=$ $S_{30}=\frac{30}{2}\left[2\right(200)+(30-1\left)50\right]$

$=15[400+1450]$

$=15\left(1850\right)$

$=27750$

Therefore, the contractor has to pay Rs $27750$ as penalty.