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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