# 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?

**Solution:**

The penalty for delay of completion by a day, Rs 200 and Rs 50 more each succeeding day.

The sum of the first n terms of an AP is given by S_{n} = n/2 [2a + (n - 1) d] or S_{n} = n/2 [a + l].

Here, a is the first term, d is a common difference and n is the number of terms.

Penalty for 1st day = Rs 200.

Penalty for 2nd day = Rs 250

Penalty for 3rd day = Rs 300

By observation, penalties are in an A.P. having the first term as 200 and common difference as 50 and number of terms as 30.

a = 200, d = 50, n = 30

Penalty that has to be paid if he has delayed the work by 30 days will be calculated as follows.

S_{n} = n/2 [2a + (n - 1) d]

S_{30} = 30/2 [2 × 200 + (30 - 1) 50]

= 15 [400 + 1450]

= 15 × 1850

= 27750

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

**Video Solution:**

## 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 the contractor has to pay as penalty if he has delayed the work by 30 days?

### Class 10 Maths NCERT Solutions - Chapter 5 Exercise 5.3 Question 15 :

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 the contractor has to pay as penalty if he has delayed the work by 30 days?

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, then money the contractor has to pay as penalty if he has delayed the work by 30 days is Rs. 27750.