A children indoor playground can accommodate 160 people in a session. Ticket price for an accompanying adult and a child is $9 and $32.50 respectively.

1. Find the total number of patrons in the afternoon session.

Number of patrons $=60\%\times160$

$=0.60\times160=96$

2. Find the numbers of children and accompanying adults.

Number of children $=75\%\times96$

$=0.75\times96=72$

Number of adults $=96-72=24$

3. Calculate the total ticket sales collected.

Total amount collected

$=72(\char36{}32.50)+24(\char36{}9)$

$=\char36{}2340+\char36{}216=\char36{}2556$

1. Recall the number of children in the afternoon session.

From part (a)(i), the playground was $60\%$ full, so the number of patrons was
$60\% \times 160 = 96.$
Since $75\%$ were children,
$75\% \times 96 = 72.$
So there were $72$ children in the afternoon.

2. Find the number of children in the evening from the children ticket sales.

Each child ticket costs $32.50.
$\text{Number of children in the evening} = \frac{3900}{32.50} = 120.$

3. Calculate the percentage increase from afternoon to evening.

$\text{Percentage increase} = \frac{120 - 72}{72} \times 100\%$
$= \frac{48}{72} \times 100\% = 66.666\ldots\%.$

1. Calculate the simple interest earned under Plan A.

For Plan A,
$I=Prt$
$I=25000\times \frac{6.2}{100}\times 2=3100$
Amount after 2 years:
$25000+3100=28100$

2. Calculate the compound amount under Plan B.

For Plan B, the quarterly rate is
$\frac{6\%}{4}=1.5\%$
There are
$2\times 4=8$
quarters in 2 years.

Amount after 2 years:
$25000(1.015)^8=2817.34$

3. Compare the two plans and justify the better return.

Plan A amount $=\char36{}28100$.

Plan B amount $=\char36{}2817.34$.

Since $2817.34<28100$, Plan A gives the better return.