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CBSE Class 10 Answered

A contract on construction job specifies penalty for delay of completion beyond a certain date as follows Rs. 200 for 1st, Rs. 250 for 2nd, and Rs. 300 for 3rd, so on. If contractor pays Rs. 27,750 as penalty, find the number of days for construction work delayed.
Asked by skandachiranjeevin | 06 Dec, 2023, 07:08: PM
answered-by-expert Expert Answer
First day penalty = Rs. 200
 
On subsequent days , penalty increases by Rs.50 .
 
Hence, penalty follows Arithmetic progression with first term a = Rs.200 and common difference  d = Rs.50 .
 
If total penalty is Rs. 27750 , then number n of days delayed is calculated from the following formula
 
Sn = ( n / 2 ) [ 2 a + ( n -1 ) d ]
 
where Sn is  sum of n terms.
 
27750 = (n/2) [ 2(200) + (n-1)50 ]
 
55500 = 400 n + 50n2 - 50n
 
50 n2 + 350 n - 55500 = 0
 
n2 + 7 n - 1110 = 0
 
(n+37)(n-30) = 0
 
Hence acceptable solution for n = 30 .
 
Number of days delayed = 30
 

Answered by Thiyagarajan K | 07 Dec, 2023, 10:15: AM

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