Question

A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each price is Rs 20 less than its proceeding price, find the value of each price.

Answer 1

HEY THERE!


Question:

A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each price is Rs 20 less than its proceeding price, find the value of each price?


Method of Solution:

Let to First term of Arithmetic Sequence or Progression="a"

Note: Here,
'a' represent first prize

Let the second prize =a-20

•°• The third prize =(a-20)-20

Sum of Prizes=700 (Given)



Let to Common difference of Arithmetic Sequence or Progression="d"

According to the Question:



Since, Value of each price Rs 20 less than its proceeding price.



So the value of price in Arithmetic Progression as common Difference =-20

Hence, Value of nth term = 7

Using Formula of Summation:


$\implies \: Sn = \frac{n}{2} (2a + (n - 1)d \\ \\ \\ S7 = \frac{7}{2} (2a + (7 - 1) - 20 = 700 \\ \\ \\ \\ \\ Sn = \frac{n}{2} (2a + (n - 1)d \\ \\ \\ S7 = \frac{7}{2} (2a + (7 - 1) - 20 = 700 \\ \\ \\ \\ \\ S7 = \frac{ \cancel{7}}{2} (2a + (7 - 1) - 20 = \cancel{700} \\ \\ \\ \implies(2a + 6( - 20) = 100 \times 2 \\ \\ \implies(2a - 120) = 200 \\ \\ \implies2a = 200 + 120 \\ \\ \\ \implies2a = 320 \\ \\ \implies \: a = \frac{320}{2} = 160$


Hence,

Let the first prize=a
=> a=160

Let the second prize =a-20
=160-20
=140

•°• The third prize =(a-20)-20
=(160-20)-20
=140-20
=120



Therefore, the value of each price 160, 140,120...

Answer 2

Hey there !!


▶ Solution :-

→ Let the first term prize be x.

•°• a = x.

→ Since the value of each prize is 20 less than its preceding price, so the value of the prizes of the prizes are in AP with common difference - ₹20 .

•°• d = - ₹ 20.

→ Number of cash prizes to be given to the students , •°• n = 7.

→ Then, the value of these prizes be ₹x , ₹( x - 20 ), ₹( x - 40 ), ...... and ₹( x - 120 ) respectively.

→ Total sum of the prizes , •°• S$\tiny 7$ = ₹700 .


▶ Now,

→ Using Identity :-

°•° S$\tiny n$ = n/2 [ 2a + ( n - 1 )d ] .

=> S$\tiny 7$ = 7/2 [ 2x + ( 7 - 1 ) (-20) ] .

=> 700 = 7/2 [ 2x + ( 6 × (-20) ) ] .

=> 700 = 7/2 [ 2x - 120 ] .

=> 700 = (7 × 2 )/2 [ x - 60 ] .

=> 7x - 420 = 700 .

=> 7x = 700 + 420 .

=> 7x = 1120 .

=> x = 1120/7 .

•°• x = 160 .


▶ Thus, the value of 1st prize = ₹160 .


✔✔ Hence, the value of each prize is ₹160, ₹140, ₹120, ₹100, ₹80, ₹60, and ₹40 . ✅✅

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THANKS


#BeBrainly.