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

A day's delay in completion carries a fine of Rs. 200 and an additional Rs 50 the next day.

We know that,

 S_n = n/2 [2a + (n - 1) d] or  S_n= n/2 [a + l].

From the given information we have,

Penalty for 1^st day = Rs. 200

Penalty for 2^nd day = Rs. 250

Penalty for 3^rd day = Rs. 300

By observation, penalties are in A.P. 

a = 200, d = 50, n = 30

Using the above information,

S_n = n/2 [2a + (n - 1)d]

S₃₀ = 30/2 [2 × 200 + (30 - 1)50]

= 15 [400 + 1450]

= 15 × 1850

= 27750

Therefore, the contractor has to pay Rs. 27750 as a penalty.