A club consists of members whose ages are in AP, 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

For arithmetic progression,

S(n) = $$\frac{n}{2}[2a + (n - 1)d]$$

Given, S(n) = 250 years; d = 3 months (or) 0.25 years; a = 7 years

Substitute the values in the above formula,

$$250 = \frac{n}{2}[2(7) + (n - 1)0.25]$$

$$500 = 14n + 0.25 n^{2} - 0.25n$$

$$ 0.25 ^{2} + 13.75 n - 500 = 0$$

After solving, we get the roots as '-80' and '25'.

we will consider only '25' as '-80' is an imaginary value.

Hence, option C is the correct answer.