NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 15

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 15

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?

Given:

Penalty for the first day = Rs 200
Penalty increases by Rs 50 each day.
Delay = 30 days

To Find:

Total penalty for 30 days delay.

Formula:

The sequence of penalties forms an arithmetic progression. 

 

The sum of an arithmetic series is given by:
Sn = n2(2a + (n-1)d)

Where:

Sn = sum of the series
n = number of terms
a = first term
d = common difference

Solution:

Here, a = 200, d = 50, n = 30

Substituting the values in the formula: Sn = n2(2a + (n-1)d)

S30 = 302(2(200) + (30-1)50)

⇒ S30 = 15(400 + 1450)

⇒ S30 = 15(1850)

⇒ S30 = 27750

Therefore, the total penalty is Rs. 27750.

Result:

The contractor has to pay Rs. 27750 as penalty.

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