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 prize.
Answers
Answer:
The value of each of the prizes was ₹ 160, ₹ 140, ₹120, ₹ 100, ₹ 80, ₹ 60 and ₹ 40.
Step-by-step explanation:
Suppose the value of 1st prize be P.
value of 2nd prize = (P − 20)
value of 3rd prize = (P − 40)
The value of these prizes are in an A.P. having common difference (d) as −20 and first term (a) as P.
a = P , d = −20
Given :
Sum of seven cash prizes, S7 = 700
By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]
S7 = 7/2 [2a + (7 – 1)d]
700 = 7/2 [2a + 6d]
700 = 7/2 × 2 [a + 3d]
700 /7 = [a + 3d]
100 = [a + 3d]
a + 3(−20) = 100
a − 60 = 100
a = 100 + 60
a = 160
value of 1st prize = P = 160
value of 2nd prize = (P − 20) = 160 - 20 = 140
value of 3rd prize = (P − 40) = 160 - 40 = 120
Hence, the value of each of the prizes was ₹ 160, ₹ 140, ₹120, ₹ 100, ₹ 80, ₹ 60 and ₹ 40.
HOPE THIS ANSWER WILL HELP YOU….
Sum of all the seven prizes is 700
Let a and d be the first term and common difference of the AP respectively
According to the question,
A prize should be 20 less than its precessor
Implies,d=-20
and let us assume that a=x
The AP would be:
x,x-20,x-40,.........
No.of terms:7 [Given]
Sum of terms:700
→n/2[2a+(n-1)d]=700
→7[2(x)+(7-1)20]=1400
→14x-840=1400
→14x=2240
→x=160
Thus the prizes would be in increasing order:
40,60,80,100,120,140,160
•First Prize:160
•Second Prize:140
•Third Prize:120