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  • 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.

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)

best_answer

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
 

Posted by

Gautam harsolia

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