Q13 of 110 Page 53

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


The amount to be paid first paid = ₹4000

It increases each day by = ₹1000


Total amount that can be paid = ₹165000


a = 4000, d = 1000, Sum = 165000


Sum of terms =


⇒ 165000 =


⇒ 165 =


⇒ 330 = n (n + 7)


⇒ n2 + 7n –330 = 0


⇒ n2 –15n + 22n –330 = 0


⇒ n(n–15) + 22(n–15) = 0


⇒ (n–15)(n + 22) = 0


⇒ n = 15 or n = –22


As negative value of n is not possible, n = 15


Therefore, number of days that construction can be delayed = 15days.


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