Question

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.

Answer 1

The penalties form an arithmetic progression (A.P.) with a first term of 200 and a common difference of 50.
\(a = 200\) and \(d = 50\)
The penalty for delaying the work by 30 days is calculated as:
= \(S_{30}\)
= \(\frac {30}{2} [2\times 200 + (30-1)50]\)
= \(15 [400 + 1450]\)
= \(15 (185\)0)
= \(27750\)

Consequently, the contractor must pay a penalty of Rs. 27750.