Question: A ferry can carry 25 trucks or 40 motorcycles at a time. If there are 15 trucks on the ferry, how many motorcycles can be loaded onto it?

Solution:
Here,
25 trucks = 40 motorcycles
∴ 1 trucks = 40/25 = 8/5 motorcycles
∴ 15 trucks = = (8 × 15)/5 = 24 motorcycles

∴ Required number of motorcycles = 40 - 24 = 16

So the ferry can carry 16 more motorcycles along with the 15 trucks.

1. Initial ratio: Milk : Water = 3 : 4
   Total mixture = 35 liters → Total parts = 3 + 4 = 7

2. Quantities in mixture:

   • Milk = $35 × \frac{3}{7} = 15$ liters

   • Water = $35 × \frac{4}{7} = 20$ liters

3. Let x = milk to be added
   New ratio Milk : Water = 1 : 1 → $\frac{15 + x}{20} = 1$

4. Solve for x:
   $15 + x = 20 \implies x = 5$

Answer: 5 liters of milk should be added.

Question: How much water should be added to 50 liters of pure milk to gain extra 12% profit when selling the mixture at the price of pure milk?

Solution:
Let’s assume,
Price of pure milk per liter = 100 Taka
So, the price of 50 liters of pure milk = 100 × 50 = 5000 Taka

Now assume,
Water added to the milk = x liters
Then the total quantity of the milk-water mixture = (50 + x) liters

Since the mixture is sold at the price of pure milk,
The selling price of (50 + x) liters = 100(50 + x) Taka

According to the question,
100(50 + x) = 5000 + 5000 এর 12%
⇒ 5000 + 100x = 5000 + {5000 × (12/100)}
⇒ 5000 + 100x = 5000 + 600
⇒ 5000 - 5000 + 100x = 600
⇒ 100x = 600
⇒ x = 600/100
⇒ x = 6

∴ Amount of water to be added = 6 liters

Shortcut:
Amount of water to be added = (Profit%/100) × Quantity of pure milk
= (12/100) × 50
= 6 liters