A wedding organizer distributed bonuses equally among his staff. If 5 more staff had been present, each person would have received Tk 50 less. But if 5 fewer staff had shown up, each person would have received Tk 75 more. How many staff members actually worked at the wedding?

Let (x) be the number of oranges sold during the on-season.

1. Off-season result

• Selling price = Tk 8
• Cost price = Tk 11
• Loss per orange = Tk (11-8=3)

For 1,800 oranges:

$\text{Off-season loss}=1800\times 3=\text{Tk }5400$

2. On-season result

• Selling price = Tk 10
• Cost price = Tk 6
• Profit per orange = Tk (10-6=4)

For (x) oranges:

$\text{On-season profit}=4x$

3. Include fixed overhead

Annual overhead:

$12\times 3000=\text{Tk }36000$

4. Require overall profit of at least Tk 5,000

$4x-5400-36000\ge 5000$

$4x-41400\ge 5000$

$4x\ge 46400$

$x\ge 11600$

Therefore, the minimum number of oranges he must sell during the on-season is

$\boxed{11,!600}$

4x-5400-36000$\ge 5000$

Let the speed of the stream be (x) km/h.

• Speed of the boat in still water = 10 km/h
• Downstream speed = (10+x) km/h
• Upstream speed = (10-x) km/h

Since the boat travels 24 km downstream and 14 km upstream in equal time,

$\frac{24}{10+x}=\frac{14}{10-x}$

Cross-multiplying,

24(10-x)=14(10+x)

240-24x=140+14x

100=38x

$x=\frac{100}{38}=\frac{50}{19}$
$x\approx 2.63$

Therefore, the speed of the stream is

$\boxed{\frac{50}{19}\text{ km/h}\approx 2.63\text{ km/h}}$

$\frac{24}{10+x}=\frac{14}{10-x}$

ধরি, দুই অঙ্কের সংখ্যাটির দশকের অঙ্ক (x) এবং এককের অঙ্ক (y)।

তাহলে সংখ্যাটি (10x+y)।

প্রথম শর্ত অনুযায়ী,

সংখ্যাটির অঙ্কদ্বয়ের যোগফলের সাথে 7 যোগ করলে তা দশকের অঙ্কের তিন গুণ হয়।

অর্থাৎ,
x+y+7=3x

y+7=2x …………… (1)

দ্বিতীয় শর্ত অনুযায়ী,

মূল সংখ্যা থেকে 18 বিয়োগ করলে অঙ্কদ্বয় উল্টে যায়।

অর্থাৎ,

10x+y-18=10y+x

9x-9y=18

x-y=2 …………… (2)

এখন, (2) থেকে

y=x-2

এটি (1)-এ বসিয়ে পাই,

(x-2)+7=2x

x=5
এবং,

y=5-2=3

সুতরাং সংখ্যাটি

10x+y=10(5)+3=53

উত্তর: $\boxed{53}$

যাচাই:

• অঙ্কদ্বয়ের যোগফল (=5+3=8), এর সাথে 7 যোগ করলে (15), যা দশকের অঙ্ক 5-এর তিন গুণ।
• (53-18=35), যা 53-এর অঙ্কদ্বয় উল্টালে পাওয়া যায়।

x+y+7=3x

10x+y-18=10y+x

First find the total wood area needed for doors and windows.

1. Doors

Each door area:

$2\times 1.25=2.5{\text{ m}}^2$

For 3 doors:

$3\times 2.5=7.5{\text{ m}}^2$

2. Windows

Each window area:

$1\times 1.25=1.25{\text{ m}}^2$

For 6 windows:

$6\times 1.25=7.5{\text{ m}}^2$

Total area required

$7.5+7.5=15{\text{ m}}^2$

3. Area of one wood piece

Each piece is:

$5\times 0.60=3{\text{ m}}^2$

4. Number of pieces required

$\frac{15}{3}=5$

Final Answer:

$\boxed{5\text{ pieces}}$