A group wanted to renovate their club. Each member contributed an amount (in Rs) equal to twice the number of members, and the government contributed an amount equal to the number of members. If each member had contributed an amount equal to the number of members and the government had given twice the number of members, they would have collected Rs 210 less. How many members are there?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 15
Write both totals in terms of the number of members \(n\); their difference is Rs 210.
Actual collection \(=n\times2n+n=2n^{2}+n\)
Other plan \(=n\times n+2n=n^{2}+2n\)
Difference \(=(2n^{2}+n)-(n^{2}+2n)=n^{2}-n=n(n-1)\)
\(n(n-1)=210=15\times14\), so \(n=15\)
The club has 15 members.