A contract on constrution job specifies a penalty for delay of co… - Vidyadip

Question

A contract on constrution job specifies a penalty for delay of completion beyond a certain date as follows: $₹ 200$ for the first day, $₹ 250$ for the second day, $₹ 300$ for the third day, etc, the penalty for each succeeding day being $₹ 50$ 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?

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Answer

The penalty is given to be:
$Rs. 200$ for the first day,
$Rs. 250$ for the second day,
$Rs.300$ for the third day, etc
Since the penalty for each succeeding day is $Rs. 50$ more than for the preceding day,
The common difference = $Rs. 50$
Consider the work to be delayed for $30$ days.
$\text{S}_\text{n}=\frac{\text{n}}{2}\big[2\text{a}+(\text{n}-1)\text{d}$
$\Rightarrow\text{S}_\text{30}=\frac{\text{30}}{2}\big[2\text{(200)}+29\text{(50)}\big]$
$\Rightarrow\text{S}_\text{30}=15\big[400+1450\big]$
$\Rightarrow\text{S}_\text{30}=27750$
Hence, the contractor has to pay $Rs. 27750$ as penalty.

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