Question

solve this question in given attachment ​

Answer 1

Here,

₹700 is to be used to give 7 cash prizes.

Let,

The value of first prize be a . Then, then value of 2nd prize ₹(a-20) , value of third prize be ₹ [(a-20)-20] and so on.

Thus,

we get an AP whose Frist term is a and common difference is -20

Since,

• S7 = 700

• $↪ \frac{7}{2} (2a + (7 - 1)( - 20)) = 700$
• $↪2a - 20 \times 6 = 700 \times \frac{2}{7}$
• $↪2a - 120 = 200$
• $↪2a = 200 + 120$
• $↪2a = 320$
• $↪a = \frac{320}{2} = 160$

Hence,

The value of first prize = ₹160

" " " second prize = ₹160 - ₹20= ₹140

" " " third prize = ₹140 - ₹20 = ₹120

" " " fourth prize = ₹120 - ₹20 = ₹100

" " " fift prize = ₹100 - ₹20 = ₹80

" " " sixth prize = ₹80 - ₹20 = ₹60

" " " seventh prize = ₹60 - ₹20 = ₹40

Answer 2

Let the value of the prices be

x, x - 20, x - 40, .....

This is an arithmetic sequence with first term (a) = x and common difference(d) =  -20.

Given,  

S7 = 700

Sn = n/2 [2a + (n - 1)d]

$\huge{\sf{=> 700 = \frac{7}{2}[2x+6(=20)]}}$

$\huge{\sf{=> 700 = \frac{7}{2}[2x-120)}}$

$\huge{\sf{=> 100 = x-60}}$

$\huge{\sf{x=160}}$

Thus, the values of the prizes are Rs. 160, Rs. 140, Rs. 120, Rs. 100, Rs. 80, Rs, 60, and Rs. 40.