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

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Penalty for the first day (a) = Rs 4000 

Increased rate for every day (d) = Rs 1000

Maximum amount of penalty (Sn

= Rs 1,65,000 

Sn = (n/2) [2a + (n - 1) 1000] 

165000 = (n/2) [2(4000) + (n – 1) 1000] 

= (n/2) [8000 + 1000 n – 1000] 

165000 = (n/2) (7000 + 1000n) 

330000 = 7000 n + 1000 n2 

0 = 1000 n2 + 7000 n – 330000 ÷ 1000 on both sides, 

n2 + 7n – 330 = 0 

(n + 22) (n – 15) = 0

n = -22 or n = 15 

n = -22 (not possible) 

∴ Maximum number of days for which the work can be delayed is 15 days.

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