A reading circle raised funds for books. Each member gave an amount (in Rs) equal to twice the number of members, and a local shop gave five times the number of members. Had each member given an amount equal to the number of members and the shop given twice the number of members, Rs 270 less would have been raised. How many members does the reading circle have?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 15
Write both totals in terms of the number of members \(n\); their difference is Rs 270.
Actual collection \(=n\times 2n+5n=2n^{2}+5n\)
Other plan \(=n\times n+2n=n^{2}+2n\)
Difference \(=n^{2}+3n=270\)
\(n=15\) gives \(15^{2}+3\times15=270\), and the difference grows as \(n\) grows, so no other positive whole number works
The number of members is 15.
Why the other options are incorrect
Option (1) 16 — Incorrect. With 16 members the difference is \(16^{2}+3\times16=304\), not Rs 270.
Option (3) 19 — Incorrect. With 19 members the difference is \(19^{2}+3\times19=418\), not Rs 270.
Option (4) 14 — Incorrect. With 14 members the difference is \(14^{2}+3\times14=238\), not Rs 270.