There are 3 doors and 6 windows in a house. Each of the doors is 2 meters long and 1.25 meters wide and each of the windows is 1 meter long and 1.25 meters wide. How many pieces of 5 meters long and 0.60 meters wide wood are required to make the doors and windows?

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

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

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

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