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Answer :
We can see, that the given penalties are in the form of A.P. having first term as 200 and common difference as 50.
Therefore, a = 200 and d = 50
Penalty that has to be paid if contractor has delayed the work by 30 days = \(S_{30}\)
By the formula of sum of nth term, we know,
\(S_n = {{n} \over {2}}[2a+(n -1)d]\)
\(S_{30}= {{30} \over {2}}[2(200)+(30 – 1)50] \)
= 15[400+1450]
= 15(1850)
= 27750
Therefore, the contractor has to pay Rs 27750 as penalty.