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A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: ₹200 for the first day, ₹ 250 for the second day, ₹300 for the third day, etc. the penalty for each succeeding day being ₹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? |
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Answer» It is given that the penalty for each succeeding day is 50 more than for the preceding day, so the amount of penalties are in AP with common difference ₹50 Number of days in the delay of the work = 30 The amount of penalties are ₹200, ₹250, ₹300,... up to 30 terms. ∴ Total amount of money paid by the contractor as penalty, S30 = ₹ 200 + ₹ 250 + ₹ 300 + ....... up to 30 terms Here, a = ₹ 200, d = ₹ 50 and n = 30 Using the formula, \(S_n=\frac{n}{2}[2a+(n-1)d],\) we get \(S_{30}=\frac{30}{2}[2\times200+(30-1)\times50]\) = 15 (400 - 1450) = 15 x 1850 = 27750 Hence, the contractor has to pay ₹27,750 as penalty |
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