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Q.

A sum of ₹ 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ₹ 20 less than its preceding prize, then what is the value of each prize?


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a

Rs.140,Rs.120,Rs.100,Rs.80,Rs.70,Rs.60 and Rs.40.

b

Rs.150, Rs.160, Rs.120, Rs.110, Rs.80, Rs.60 and Rs.50.

c

Rs.160,Rs.140,Rs.120,Rs.100,Rs.80,Rs.60 and Rs.40.

d

Rs.165,Rs.145,Rs.125,Rs.105,Rs.85,Rs.65 and Rs.45.  

answer is C.

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Detailed Solution

Given that the value of each prize is ₹20 less than its preceding prize, so the values of the prizes are in AP with a common difference -20.
Therefore, d = -20.
Let the value of the first prize be Rs.a.
Also, given the total sum of the prizes, S 7 =700 .
Formula used for sum of first n term of A.P.:
S n = n 2 [2a+(n−1)d]
Applying sum of n terms of an A.P. formula:
∴ S 7 = 7 2 [2a+(7−1)×(−20)] ⇒700= 7 2 ×(2a−120) ⇒700=7a−420 ⇒7a=1120 ⇒a=160 Therefore, the value of the first prize is Rs.160.
Hence, the value of each prize is Rs.160,Rs.140,Rs.120,Rs.100,Rs.80,Rs.60 and Rs.40.
Hence, option (3) is correct.
 
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