Question: A train running at a certain speed crosses a 496-meter-long platform in 56 seconds. If the length of the train is 560 meters, how long will it take to cross a bridge that is 100 meters in length?

Solution:
We know,
When a train crosses any object, it covers a distance equal to the sum of the object's length and its own length.

So, when crossing a platform, the distance covered by the train = (496 + 560) meters = 1056 meters
And
when crossing a bridge, the distance covered by the train = (100 + 560) meters = 660 meters

Now,
The train covers 1056 meters in = 56 seconds
∴ It covers 1 meter in = (56/1056) seconds
∴ It covers 660 meters in = (56 × 660)/1056 seconds = 35 seconds

Question: The speed of a boat in still water is 6 km/h. The time it takes to travel downstream is half the time it takes to travel upstream. What is the speed of the stream?

Solution:
Let the speed of the current be = x km/h

Then,
Downstream speed = (6 + x) km/h
Upstream speed = (6 − x) km/h

According to the question:
(6 + x) = 2(6 − x)
⇒ 6 + x = 12 - 2x
⇒ 2x + x = 12 - 6
⇒ 3x = 6
⇒ x = 6/3
⇒ x = 2

∴ The speed of the current = 2 km/h

আসো দ্রুত যাচাই করি:

• প্রাথমিকভাবে তামা = $12$ গ্রাম, দস্তা = $3$ গ্রাম।

• যদি আরও $k$ গ্রাম তামা যোগ করি, তবে নতুন অনুপাত হবে:

$$\frac{12+k}{3} = \frac{5}{1}$$ $$12+k = 15 \quad \Rightarrow \quad k = 3$$

✅ সঠিক!

অতএব, আরো ৩ গ্রাম তামা মেশাতে হবে যাতে তামা ও দস্তার অনুপাত ৫:১ হয়।