The speed of a boat in still water is 10 km per hour. If it can travel 24 km downstream and 14 km in the upstream in equal time, calculate the speed of the flow of stream.

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 actual number of staff members be (n), and let each person actually receive Tk (x).

Then the total bonus amount is

nx

Condition 1: 5 more staff members

If there had been (n+5) staff, each would have received Tk 50 less:

(n+5)(x-50)=nx

Expanding:

nx+5x-50n-250=nx

5x=50n+250

x=10n+50

Condition 2: 5 fewer staff members

If there had been (n-5) staff, each would have received Tk 75 more:

(n-5)(x+75)=nx

Expanding:

nx+75n-5x-375=nx

5x=75n-375

x=15n-75

Equating the two expressions for (x)

10n+50=15n-75

125=5n

n=25

Therefore, the number of staff members who actually worked at the wedding was

$\boxed{25}$

10n+50=15n-75

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:

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