The members of a cricket club decided to buy new equipment. Each member gave an amount (in Rs) equal to twice the number of members, and a sponsor gave an amount equal to the number of members. Had each member given an amount equal to the number of members and the sponsor given twice the number of members, the collection would have been Rs 342 less. How many members does the club have?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 19
Write both totals in terms of the number of members \(n\); their difference is Rs 342.
Actual collection \(=n\times 2n+n=2n^{2}+n\)
Other plan \(=n\times n+2n=n^{2}+2n\)
Difference \(=n^{2}-n=342\)
\(n=19\) gives \(19^{2}-19=342\), and the difference grows as \(n\) grows, so no other positive whole number works
The number of members is 19.
Why the other options are incorrect
Option (2) 18 — Incorrect. With 18 members the difference is \(18^{2}-18=306\), not Rs 342.
Option (3) 20 — Incorrect. With 20 members the difference is \(20^{2}-20=380\), not Rs 342.
Option (4) 23 — Incorrect. With 23 members the difference is \(23^{2}-23=506\), not Rs 342.