Question: What is the difference between simple and compound interest at 10% per annum on a sum of Tk. 6000 at the end of 2 years?

Solution:
Principal (P) = Tk. 6000
Rate (r) = 10% per annum
Time (n) = 2 years

Simple Interest (SI):
SI = (P × R × T)/100
= (6000 × 10 × 2)/100
= 120000/100
= Tk. 1200

Compound Interest (CI):
Amount (A) = P × (1 + r/100)n
= 6000 × (1 + 10/100)2
= 6000 × (1.1)2
= 6000 × 1.21
= Tk. 7260

∴ CI = A - P = 7260 - 6000
= Tk. 1260

∴ Difference between CI and SI = 1260 - 1200
= Tk. 60

Question: A certain principal amount, invested at simple interest, grows to Tk. 950 after 3 years and Tk. 1010 after 4 years. What is the original principal amount?

Solution:
Given,
Amount after 3 years = Tk. 950
Amount after 4 years = Tk. 1010
∴ Interest for 1 year = 1010 - 950 = Tk. 60

∴ Interest for 3 years = 60 × 3 = Tk. 180

∴ Principal = 950 - 180 = Tk. 770

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