Algebra
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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, then number of members in the club are:

 A.

18

 B.

20

 C.

25

 D.

24

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Solution:
Option(C) is correct

Let $n$ be the number of members in the club

Then,

\(250=\dfrac{n}{2}[2\times 7+(n-1)\times \dfrac{3}{12}]\)

\(n=25\)

Edit: A typo in the solution has been corrected after it was pointed out by Sravan Reddy.

Edit 2: For a speed trick​ to solve the question, check comment by Sravan Reddy.


(4) Comment(s)


Sravan Reddy
 ()

@Admin: Small correction in formula but calculation is correct - It should be (n-1) instead of (n+1) in the formula :)

Some speed trick to other friends: Write the equation and arrive at the answer by checking options. 

Here $\dfrac{(n-1)*1}{4}$ should be a whole number - so option subtracted by 1 should be a multiple of 4. 

So, 25 is the only odd number and is the answer.


Deepak
 ()

Thank you Sravan, for letting me know about the error, corrected it.


Vikas
 ()

how does the 3/12 came ????


Rahul
 ()

as the values are given in years and d=3 MONTHS (not years)....so 3/12 years