A street vendor sells oranges throughout the year. During the off-seasons, he sells each orange for Tk 8 but his cost price is Tk 11 per orange. During the on-seasons, his cost price drops to Tk 6 per orange and he sells each one for Tk 10. His fixed monthly overhead costs are Tk 3,000. In a particular year, he sells 1,800 oranges during the 4 off-season months and must sell enough oranges during the remaining 8 on-season months to end the year with an overall profit of at least Tk. 5,000. What is the minimum number of oranges he must sell during on-season to achieve this?

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

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:

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