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.
Solution:- Value of 1st prize = ₹x
∵ Value of each prize is Rs 20 less than its preceding prize,
∴ Value of 2nd prize
= ₹(x - 20)
∴ Value of 3rd prize
= (x - 20) - 20
= ₹(x - 40)
*So value of prizes are..
x, x - 20, x - 40...
*Clearly this forms an AP with,
a = x d = -20
∵ There are total seven prizes,
∴ n = 7
➙ The sum of the prizes is Rs 700,
∴ Sₙ = 700
*Using formula, Sₙ =
n
/
2
[2a + (n - 1)d] ∴
n
/
2
[2a + (n - 1)d] = 700 ∴
7
/
2
[2(x) + (7 - 1)(-20)] = 700 ∴ 2x + (6)(-20) =
700 × 2
/
7
∴ 2x - 120 = 200
∴ 2x = 200 + 120
∴ 2x = 320
∴ x =
320
/
2
∴ x = 160
Therefore,
*Value of 1st prize
= x
= ₹160
*Value of 2nd prize
= x - 20
= 160 - 20
= ₹140
*Value of 3rd prize
= x - 40
= 160 - 40
= ₹120
*Value of 4th prize
= x - 60
= 160 - 60
= ₹100
*Value of 5th prize
= x - 80
= 160 - 80
= ₹80
*Value of 6th prize
= x - 100
= 160 - 100
= ₹60
*Value of 7th prize
= x - 120
= 160 - 120
= ₹40
Hence,
The prizes are ₹160, ₹140, ₹120, ₹100, ₹80, ₹60, and ₹40.
------------------------------------
Try This..
✒ 8 terms of an AP add up to 0. If the 1st term is -7 and the last is 7, find the common difference.
✒ The sum of 6 terms of an AP is 90. If the first term is 5, find the common difference.
✒ A sum of ₹1000 is to be divided among 5 people in AP. If the smallest share is ₹100, find all the shares.
❌ Common Mistakes
Misidentifying the common difference:▸ If each term is less than the previous one, the common difference is negative.Incorrect formula usage:▸ Double-check whether you're using the correct formula for the sum of AP terms.Wrong substitution of values:▸ Simple arithmetic errors can cost marks. Be careful with signs, especially negative values.Not verifying total:▸ Always check if the sum of your AP terms adds up to the given total.
📝 Related Questions:-
- Ex 5.3 Q4 - How many terms of the AP: 9, 17, 25,... must be taken to give a sum of 636?
- 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 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?
Queries Solved:-
Class 10 Ex 5.3
Ex 5.3 Q16 Class 10
Class 10 Ex 5.3 Q16
Class 10 Chap 5 Ex 5.3 Q16
Class 10 Arithmetic Progression
If you found it helpful, please leave a comment below sharing your thoughts or questions.
Don’t forget to share it with your classmates to help them learn too.
Good luck, and happy learning!
Together, let’s make math simpler and more enjoyable for everyone!