For a school trip, each student paid an amount (in Rs) equal to three times the number of students, and the school added twice the number of students. If instead each student had paid twice the number of students and the school had added four times the number of students, the collection would have been Rs 360 less. How many students went on the trip?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 20
Write both totals in terms of the number of students \(n\); their difference is Rs 360.
Actual collection \(=n\times 3n+2n=3n^{2}+2n\)
Other plan \(=n\times 2n+4n=2n^{2}+4n\)
Difference \(=n^{2}-2n=360\)
\(n=20\) gives \(20^{2}-2\times20=360\), and the difference grows as \(n\) grows, so no other positive whole number works
The number of students is 20.
Why the other options are incorrect
Option (2) 21 — Incorrect. With 21 students the difference is \(21^{2}-2\times21=399\), not Rs 360.
Option (3) 24 — Incorrect. With 24 students the difference is \(24^{2}-2\times24=528\), not Rs 360.
Option (4) 19 — Incorrect. With 19 students the difference is \(19^{2}-2\times19=323\), not Rs 360.