Question: How much water should be added to 80 liters of pure milk to gain extra 20% 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 × 80 = 8000 Taka

Now assume,
Water added to the milk = x liters
Then the total quantity of the milk-water mixture = (80 + x) liters

Since the mixture is sold at the price of pure milk,
The selling price of (80 + x) liters = 100(80 + x) Taka

According to the question,
100(80 + x) = 8000 + 8000 of 20%
⇒ 8000 + 100x = 8000 + {8000 × (20/100)}
⇒ 8000 + 100x = 8000 + 1600
⇒ 8000 - 8000 + 100x = 1600
⇒ 100x = 1600
⇒ x = 1600/100
⇒ x = 16

∴ Amount of water to be added = 16 liters

Question: 60% of a number is 30 less than three-fourth of the same number. Find the number.

Solution:
Let,
the number = x.

ATQ,
60% of x = (3/4) of x - 30
⇒ 60x/100 = (3x/4) - 30
⇒ 3x/5 = (3x/4) - 30
⇒ (3x/4) - (3x/5) = 30
⇒ (15x - 12x)/20 = 30
⇒ 3x/20 = 30
∴ x = 200

So, the number is 200.

Solution:
Given,
Principal, P = 30000
Rate, r = 7% per annum
Compound Interest, CI = 4347

We know,
Amount, A = P + CI = 30000 + 4347 = 34347

Using the compound amount formula:
A = P(1 + r/100)n
⇒ 34347 = 30000 × (1 + 7/100)n
⇒ 34347 = 30000 × (107/100)n
⇒ (107/100)n = 34347/30000
⇒ (1.07)n = 1.1449
⇒ (1.07)n = (1.07)2
∴ n = 2 years