By increasing the price of an entry ticket to a fair in the ratio 9:13, the number of visitors to the fair has decreased in the ratio 7:4. In what ratio has the total collection increased or decreased?
- Aincreased in the ratio 52:63
- Bincreased in the ratio 36:91
- Cdecreased in the ratio 63:52
- Ddecreased in the ratio 91:36
Solution & Step-by-step Explanation
The total collection of a fair is determined by:
Total Collection=Price of ticket×Number of visitors
Let the initial price of the ticket be 9p and the final price be 13p.
Let the initial number of visitors be 7v and the final number of visitors be 4v.
Initial Collection=9p×7v=63pv
Final Collection=13p×4v=52pv
Ratio of initial collection to final collection:
Ratio=
52pv
63pv
=
52
63
Since 63>52, the total collection has decreased.
The collection decreased in the ratio 63:52.
Total Collection=Price of ticket×Number of visitors
Let the initial price of the ticket be 9p and the final price be 13p.
Let the initial number of visitors be 7v and the final number of visitors be 4v.
Initial Collection=9p×7v=63pv
Final Collection=13p×4v=52pv
Ratio of initial collection to final collection:
Ratio=
52pv
63pv
=
52
63
Since 63>52, the total collection has decreased.
The collection decreased in the ratio 63:52.