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# 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:

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.

To do:

We have to find the money the contractor has to pay as penalty, if he has delayed the work by 30 days.

Solution:

Let the penalty for first day be $a_1$, second day be $a_2$ so on and number of days be $n$.

$a_1=a=200, a_2=250$

$d=a_2-a_1=250-200= 50$

$n=30$

We know that,

$S_{n}=\frac{n}{2}[2 a+(n-1) d]$

Therefore,

$S_{30}=\frac{30}{2}[2 a+(30-1) d]$

$=15[2 \times 200+29 \times 50]$

$=15[400+1450]$

$=15 \times 1850$

$=Rs.\ 27,750$

**The money the contractor has to pay as penalty is Rs. 27750.**