A club consists of members whose ages are in A P the common difference being 3 months If the younges...........

Quantitative Aptitude ( CCS) Number System

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 is

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Explanation:

As per the question,
d=3(months)
a=7(years)=7×12=84(months).
S(n)=250(years)=250*12=3000(months)

S(n)=n/2(2a+(n-1)d).
=3000=n/2(2*84+(n-1)3.
=3000*2=n(168+3n-3).
=6000=n(165+3n).
=6000=165n+3n^2.
=3n^2+165n-6000=0.
=3(n^2+55n-2000)=0.
=n^2+55n-2000=0/3=0.
=n^2+80n-25n-2000=0.
=n(n+80)-25(n+80)=0.
=(n-25)(n+80)=0.
We'll discard (n+80) as it gives-ve value.
n-25=0.
=n=25.

There are 25 members in the club.

Hence, there is option 3 is the correct answer.