Question

A contract on a 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 does the contractor have to pay as a penalty  if he has delayed the work by 30 days.

Answer 1

Here, penalty for delay on

1^th day = 200

2^nd day = 250

3^rd day = 300

Now, 200, 250, 300, etc. are in AP such that a = 200,

d = 250 - 200 = 50

S₃₀ is given by

S₃₀ = `30/2 [2 (200) + (30 - 1)xx50]`      ..[using, `S_n = n/2 [2a + (n -1)]d`]

= 15 [400 + 29 × 50]

= 15 [400 + 1450]

= 15 × 1850

= 27,750

Thus, a penalty for the delay for 30 days is < 27,750.