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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.


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Solution

As it has been given in the question that the penalty for each succeeding day being Rs.50 more than for the preceding day. This condition is in the form of an Arithematic progression (A.P.) Such that

200,250,300,350,400,andsoon

Where a=200andd=50.

Now, we need to find the penalty if the work is delayed by 30 days. Therefore, n=30

We know that the sum of an A.P.

Sn=n22a+n-1dS30=3022×200+30-150S30=15×1850S30=27750

Hence, the total penalty given by the contractor is 27750.


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