Advertisements
Advertisements
प्रश्न
A sum of ₹2800 is to be used to award four prizes. If each prize after the first is ₹200 less than the preceding prize, find the value of each of the prizes
Advertisements
उत्तर
Let the amount of the first prize be ₹a
Since each prize after the first is ₹200 less than the preceding prize, so the amounts of the four prizes are in AP.
Amount of the second prize = ₹ (a - 200)
Amount of the third prize = ₹ (a - 2 × 200) = (a-400)
Amount of the fourth prize = ₹(a -3 × 200) =(a-600)
Now,
Total sum of the four prizes = 2,800
∴ ₹a + ₹(a -200) + ₹ (a - 400) + ₹(a - 600) = ₹2,800
⇒ 4a - 1200 = 2800
⇒ 4a = 2800 + 1200 = 4000
⇒ a= 1000
Amount of the first prize = ₹1,000
Amount of the second prize = ₹ ( 1000 - 200) =₹800
Amount of the third prize = ₹( 1000 = 400) = ₹600
Amount of the fourth prize = ₹(1000-600) = ₹400
Hence, the value of each of the prizes is ₹1,000, ₹800, ₹600 and ₹400.
APPEARS IN
संबंधित प्रश्न
Find the sum of the following APs.
`1/15, 1/12, 1/10`, ......, to 11 terms.
Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
Find the sum of the odd numbers between 0 and 50.
Which term of the progression 20, 19`1/4`,18`1/2`,17`3/4`, ... is the first negative term?
Find the sum of the following arithmetic progressions:
−26, −24, −22, …. to 36 terms
Find the sum of all odd numbers between 100 and 200.
Find the sum of the first 40 positive integers divisible by 3
Which term of the A.P. `20, 19 1/4, 18 1/2, 17 3/4,` ..... is the first negative term?
The sum of first three terms of an AP is 48. If the product of first and second terms exceeds 4 times the third term by 12. Find the AP.
The sum of the first n terms in an AP is `( (3"n"^2)/2 +(5"n")/2)`. Find the nth term and the 25th term.
The nth term of an AP is given by (−4n + 15). Find the sum of first 20 terms of this AP?
Find the first term and common difference for the A.P.
127, 135, 143, 151,...
Kargil’s temperature was recorded in a week from Monday to Saturday. All readings were in A.P. The sum of temperatures of Monday and Saturday was 5°C more than sum of temperatures of Tuesday and Saturday. If temperature of Wednesday was –30° celsius then find the temperature on the other five days.
Choose the correct alternative answer for the following question .
In an A.P. 1st term is 1 and the last term is 20. The sum of all terms is = 399 then n = ....
Q.5
How many terms of the A.P. 25, 22, 19, … are needed to give the sum 116 ? Also find the last term.
If the sum of first n terms of an AP is An + Bn² where A and B are constants. The common difference of AP will be ______.
The sum of first ten natural number is ______.
Kanika was given her pocket money on Jan 1st, 2008. She puts Rs 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continued doing so till the end of the month, from this money into her piggy bank. She also spent Rs 204 of her pocket money, and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month?
Find the sum of all even numbers from 1 to 250.
