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Q.

A club consists of members whose ages are in A.P., the  common difference being 3 months. If the youngest  member of the club is just 7 years old and the sum  of the ages of all the members is 250 years, then the  number of members in the club are

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a

15

b

25

c

20

d

30

answer is B.

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Detailed Solution

Sn=n2[2a+(n−1)d]Here a = 1st term = 7 years, d = 3 months = 14 year,Sn=250∴ 250=n22×7+(n−1)×14⇒ 250=n2n+554⇒ 2000=n2+55n⇒ n2+55n−2000=0⇒ (n−25)(n+80)=0⇒n=25.∴ Number of members in the club = 25.
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