A contract on 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 penalty, if he has delayed the work by 30 days?
Solution:
We can see, that the given penalties are in the form of AP with the first term as 200 and the common difference as 50.
Therefore, a = 200 and d = 50
The penalty that has to be paid if the contractor has delayed the work by 30 days = S 30
By the formula of the sum of n terms, we know,
Sn = n /2[2a + (n – 1) d ]
Therefore,
S 30= 30/2[2(200) + (30 – 1)50]
= 15[400 + 1450]
= 15(1850)
= 27750
Therefore, the contractor has to pay ₹ 27750 as a penalty.