Q : 16         A sum of Rs \small 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 \small 20 less than its preceding prize, find the value of each of the prizes.

Answers (1)

It is given that
Each price is decreased by 20 rupees, 
Therefore,  d = -20 and there are total 7 prizes so n = 7 and sum of prize money is Rs 700 so S_7 = 700
Let a be the prize money given to the 1st student
Then,
S_7 = \frac{7}{2}\left \{ 2a+(7-1)(-20) \right \}
700 = \frac{7}{2}\left \{ 2a-120 \right \}
2a - 120 = 200
a = \frac{320}{2}= 160
Therefore, the prize given to the first student is Rs 160
Now,
Let a_2,a_2,...,a_7 is the prize money given to the next 6 students
then,
a_2 = a+d = 160+(-20)=160-20=140
a_3 = a+2d = 160+2(-20)=160-40=120  
a_4 = a+3d = 160+3(-20)=160-60=100
a_5 = a+4d = 160+4(-20)=160-80=80
a_6 = a+5d = 160+5(-20)=160-100=60
a_7 = a+6d = 160+6(-20)=160-120=40
Therefore, prize money given to 1 to 7 student is 160,140,120,100,80,60.40
 

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