Question

16, 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

160,140,120,100,80, 60 ,40

Step-by-step explanation:

let first prize be Rs x ,

other six prizes would be (x - 20), (x - 40) , (x - 60) ,( x - 80) , (x - 100) ,(x - 120)

sum of all prizes = 700

7x - 420 = 700 => x = 160

value of each of the prizes

160, 140 , 120 , 100 , 80, 60, 40

Answer 2

$\large\bf\underline{Given:-}$

• Rs 700 is used to give seven cash prizes to students.
• cost of each prize is Rs 20 less than it's preceding prize

$\large\bf\underline {To \: find:-}$

• Value of prizes.

$\huge\bf\underline{Solution:-}$

• Let the Cost of 1st prize be x

It is given in the Question that the cost of each prize is 20 less than it's preceding prize, then,

• Cost of 2nd prize = x - 20
• cost of 3rd prize = (x- 20)-20 = x- 40
• cost of 4th prize = (x - 40) -20 = x - 60

So, we get a series of AP:-

• x , x - 20, x - 40, x - 60...

• first term (a) = x
• common difference (d) = -20

• Sum of 7 Prizes is given = 700

we know that,

$\large \bigstar \tt \: S_n = \frac{n}{2} \big\{2a + (n - 1)d \big \}$

• sn = 700
• a = x
• n = 7
• d = -20

$\tt \rightarrowtail \: 700 = \frac{7}{2} \big \{ 2x + (7 - 1) \times ( - 20)\big \} \\ \\ \tt \rightarrowtail \cancel{700} \times \frac{2}{ \cancel7} = \big \{2x + 6 \times ( - 20) \big \} \\ \\ \tt \rightarrowtail \:100 \times 2= \big \{2x - 120 \big \} \\ \\ \tt \rightarrowtail \:200 = 2x - 120 \\ \\ \tt \rightarrowtail \:200 + 120 = 2x \\ \\ \tt \rightarrowtail \:320= 2x \\ \\ \tt \rightarrowtail \:x = \cancel\dfrac{320}{2} \\ \\ \rightarrowtail \boxed{ \tt \: x = 160}$

Cost of 1st prize x = Rs 160

Cost of 2nd prize x - 20 = 160 - 20 = 140

cost of 3rd prize x- 40 = 160 - 40 = 120

cost of 4th prize x - 60 = 160 -60 = 100

cost of 5th prize x - 80 = 160 - 80 = 80

Cost of 6th prize x - 100 = 160 - 100 = 60

Cost of 7th prize x - 120 = 160 - 120 = 40

Hence,

✝️ cost of all 7 Prizes = 160, 140, 120, 100, 80 , 60, 40

$\rule{200}3$