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(D) It can be observed that these penalties form an Arithmetic Progression $(A.P.)$ with the first term $a = 200$ and common difference $d = 50$.The n

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$27750$

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(D) It can be observed that these penalties form an Arithmetic Progression $(A.P.)$ with the first term $a = 200$ and common difference $d = 50$.The number of days is $n = 30$.The total penalty to be paid is the sum of the first $30$ terms of the $A.P.$,given by the formula $S_n = \frac{n}{2}[2a + (n - 1)d]$.Substituting the values:$S_{30} = \frac{30}{2}[2(200) + (30 - 1)50]$$S_{30} = 15[400 + 29 	imes 50]$$S_{30} = 15[400 + 1450]$$S_{30} = 15[1850]$$S_{30} = 27750$Therefore,the contractor has to pay ₹ $27750$ as a penalty.

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