Question

A construction company will be penalised each day for delay in construction of a bridge. The penalty will be₹ 4000 for the first day and will increase by ₹ 1000. for each following day. based on its budget, the company can afford to pay a maximum of ₹1,65,000 towards penalty. Find the maximum number of days by which the completion of work can be delayed

Answer 1

So the penalty issued every day is an increasing A.P. let us take first term of the A.P. be a=₹4000 and common difference d=₹1000. Sum of n terms in an A.P. =n/2(1st term +nth term ). So let's take sum of nth terms of this A.P.= ₹165000=> 165000=n/2(4000+4000+(n-1)1000)=> 165000=n/2(n+7000)
=> 330000=n(n+7000) =>
${n}^{2} + 7000n - 330000 = 0$
=> n=96 days approximately .Hope it helps you...