A club had ₹195 in its fund. After each member of the club contributed an amount equal to the number of members, the total money in the club was equally divided among all members, and each received ₹28. Find the number of members in the club.

Q.A club had ₹195 in its fund. After each member of the club contributed an amount equal to the number of members, the total money in the club was equally divided among all members, and each received ₹28. Find the number of members in the club.

Let the number of members in the club be \(x\). \(\therefore\) If each member contributes ₹\(x\), the total contribution is \(x \times x = x^2\) rupees. The club already had ₹195. \(\therefore\) Total amount in the club = ₹\((x^2 + 195)\) According to the condition, \[ x^2 + 195 = 28x \] or, \[ x^2 - 28x + 195 = 0 \] or, \[ x^2 - (15 + 13)x + 195 = 0 \] or, \[ x^2 - 15x - 13x + 195 = 0 \] or, \[ x(x - 15) - 13(x - 15) = 0 \] or, \[ (x - 15)(x - 13) = 0 \] So, either \(x - 15 = 0\) i.e., \(x = 15\), or \(x - 13 = 0\) i.e., \(x = 13\) \(\therefore\) The number of members can be either 15 or 13.