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?
Penalty for delay for first day = Rs. 200
Penalty for delay for second day = Rs. 250
Penalty for delay for third day = Rs. 300
Penalty for each succeeding day is Rs. 50 more than for the preceding day.
∴ The amount of penalties are in AP with common difference
= d = Rs.50
Also, number of days in delay of the work = 30 days
Thus the penalties are 200, 250, 300, … up to 30 terms
Thus the amount of money paid by the contractor is 200 + 250 + 300 + … up to 30 terms
Here, first term = a = 200
Common difference = d = 50
Number of terms = n = 30
∴ The sum = S30 = (30/2) × [2(200) + (30 - 1)(50)]
= 15 × [400 + 1450]
= 15 × 1850
= 27750
Thus the total amount of money paid by the contractor = Rs. 27750