A contract on the construction 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 the penalty if he has delayed the work by 30 days?

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27,750

29,750

28,750

25,750

answer is B.

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Detailed Solution

It is given that, the penalty is 200 for the first day, 250 for the second day, and 300 for the third day.
So,
200, 250, 300, ….
Above is in the form of an AP.
Here,

a = 200 d = 250 − 200 d = 50

The number of days delay for the work is 30, so, n = 30.
The total amount paid by the contractor as the penalty is,

S n = n 2 [2 a + (n − 1) d]

On putting given values in above we get,

S 30 = 302 [2 (200) + (30 − 1) 50]

= 15 [400 + 29 (50)]

= 15 (1850)

= 27, 750

So, the contractor has to pay ₹27,750 as a penalty.
Option 2) is correct.

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