Question

A contact on a construction job specifies a penalty for delay of completion beyond a certain date as follows, Rs. 200 for the first day, Rs. 300 for the second day, Rs. 400 for the third and so on if the total payment is Rs.2000 How many days did the contract has been delayed if no net money is transferred?

Answer 1

There is no net money transferred so

$⟹\text{penalty}=\text{Income}$

The penalty forms an $AP$ with $a=200;d=300-200=100$

Let the work be delayed for $n$ days

So the total penalty is $\frac{n}{2}\left[2\right(200)+(n-1\left)100\right]2000=\frac{n}{2}[400+100n-100]4000=100n(3+n)n^2+3n=40n^2+3n-40=0n^2+8n-5n-40=0n(n+8)-5(n+8)=0(n+8)(n-5)=0n=-8,5$

So the no.of days $=5$