Question

A sum of Rs.700 is to be used to gI've 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 .

Only by using the formula :--

S
$= \frac{n}{2} (2a + (n - 1)d)$
​

Answer 1

GIVEN :-

• Total prize money = Rs700.
• The prize money is to be distributed among 7 students such that each prize is 20 less thn the preceding prize.

TO FIND :-

• Value of each prize.

TO KNOW :-

$\\ \boxed{\boxed{ \bf \: s_{n} = \dfrac{n}{2} \{2a + (n - 1)d \} }}$

Here ,

• S{n} → Sum of 'n' terms
• n → number of terms
• a → 1st term
• d → Common difference

SOLUTION :-

We know , each prize is 20 less than its preceding prize.

let the seven prizes be (x) , (x-20) , (x-40) , (x-60) , (x-80) , (x-100) , (x-120)

Sumof all the terms is 700.

According to question ,

• a = x
• n = 7
• d = -20
• s{7} = 700

Putting values in formula , we get...

$\\ \implies \sf \: 700 = \dfrac{7}{2} \{2(x) + (7 - 1)( - 20) \} \\ \\ \implies \sf \: 700 \times 2 = 7 \{2x + (6)( - 20) \} \\ \\ \implies \sf \: 1400 = 7(2x - 120) \\ \\ \implies \sf \: \cancel\dfrac{1400}{7} = 2x - 120 \\ \\ \implies \sf \: 200 = 2x - 120 \\ \\ \implies \sf \: 200 + 120 = 2x \\ \\ \implies \sf \: 320 = 2x \\ \\ \implies \boxed{\sf \: x = 160}$

Hence , Prizes are :-

• x = 160
• x-20 = 140
• x-40 = 120
• x-60 = 100
• x-80 = 80
• x-100 = 60
• x-120 = 40

Hence , Prizes are 160Rs , 140Rs , 120Rs , 100Rs , 80Rs , 60Rs , 40Rs respectively.