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 prize is rs 20 less than its preceding prize find the value of each of the prizes.

Answer 1

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 77 = ₹700 .


▶ Now,

→ Using Identity :-

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

=> S\tiny 77 = 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.

Answer 2

Answer:

Let the cost of 1st prize be P.

Cost of 2nd prize = P − 20

And cost of 3rd prize = P − 40

It can be observed that the cost of these prizes are in an A.P. having

common difference as −20 and first term as P.

a = P and d = −20

Given that, S7 = 700

7/2[2a+(7-1) d] = 700

a + 3(−20) = 100

a − 60 = 100

a = 160

Therefore, the value of each of the prizes was Rs 160, Rs 140, Rs 120,

Rs 100, Rs 80, Rs 60, and Rs 40.

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