Ex 5.3 Q15 - 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?
Solution:-Given,
*Penalty for 1st day = ₹200
Penalty for 2nd day = ₹250
Penalty for 3rd day = ₹300
*Penalty for each succeeding day is ₹50 more than the preceding day.
➙ Since, no. of delayed days for work is 30,
∴ The amount to be paid in each penalty is..
200, 250, 300...upto 30 terms
*Clearly this forms an AP with,
a = 200 d = 50
∴ Total amount paid by the contractor as penalty is,
200 + 250 + 300 + ... + upto 30 terms
∴ S₃₀ = 200 + 250 + 300 + ... + upto 30 terms
*Using formula, Sā =
n
/
2
[2a + (n - 1)d] ∴ S₃₀ =
30
/
2
[2(200) + (30 - 1)50] = 15[400 + (29)50]
= 15(400 + 1450)
= 15(1850)
= 27750
∴ S₃₀ = 27750
Hence,
The contractor has to pay ₹27750 as the penalty if he has delayed the work by 30 days.
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Try This..
✒ A student returns a library book 15 days late. The fine is ₹10 on the first day, ₹15 on the second day, ₹20 on the third, and so on. What is the total fine?
✒ A staircase has steps increasing in width by 2 cm. The first step is 10 cm wide, the second 12 cm, and so on. What is the total width after 25 steps?
✒ Ravi saves ₹5 on the first day, ₹10 on the second day, ₹15 on the third day, and so on. How much will he save in 20 days?
❌ Common Mistakes
Wrong common difference (d):▸ Always subtract the first term from the second.Misusing the formula:▸ Don’t confuse AP sum with geometric series or use wrong values.Calculation errors:▸ Recheck multiplication and bracket operations, especially with big numbers.Using wrong number of terms (n):▸ Make sure you’re clear on how many terms are involved (in this case, 30 days = 30 terms).
š Related Questions:-
- Ex 5.3 Q6 - The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?
- Ex 5.3 Q16 - A sum of ₹700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ₹20 less than its preceding prize, find the value of each of the prizes.
Queries Solved:-
Class 10 Ex 5.3
Ex 5.3 Q15 Class 10
Class 10 Ex 5.3 Q15
Class 10 Chap 5 Ex 5.3 Q15
Class 10 Arithmetic Progression
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