Question: The ratio of the present ages of a mother and son is 7 : 2. After 7 years, the ratio of their ages becomes 8 : 3. What will be the ratio of their ages after 11 years?

Solution:
Let,
The present age of the mother = 7x years
The present age of the son = 2x years

After 7 years, their ages will be:
Mother = (7x + 7) years
Son = (2x + 7) years

According to the question,
(7x + 7)/(2x + 7) = 8/3
⇒ 3(7x + 7) = 8(2x + 7)
⇒ 21x + 21 = 16x + 56
⇒ 21x - 16x = 56 - 21
⇒ 5x = 35
⇒ x = 35/5
∴ x = 7

Present age of mother = 7 × 7 = 49 years
Present age of son = 2 × 7 = 14 years

Now, after 11 years,
Mother's age = 49 + 11 = 60 years
Son's age = 14 + 11 = 25 years

∴ The ratio of their ages after 11 years,
= 60 : 25
= 12 : 5

Question: A mixture contains copper, zinc, and tin in the ratio 2 : 3 : 5. If the total weight of the mixture is 50 grams, how many grams of tin are there in the mixture?

Solution:
Given,
Copper : Zinc : Tin = 2 : 3 : 5

Total parts = 2 + 3 + 5 = 10

Weight of tin = (5/10) × 50 = 25 grams

Question: What is the difference between simple and compound interest at 10% per annum on a sum of Tk. 5,000 at the end of 2 years?

Solution:
Principal (P) = Tk. 5,000
Rate (R) = 10% per annum
Time (T) = 2 years

Simple Interest (SI):
SI = (P × R × T)/100
= (5000 × 10 × 2) / 100
= 100000/100
= Tk. 1000

Compound Interest (CI):
Amount (A) = P × (1 + R/100)^T
= 5000 × (1 + 10/100)²
= 5000 × (1.1)²
= 5000 × 1.21
= Tk. 6050

∴ CI = A - P = 6050 - 5000
= Tk. 1050

∴ Difference between CI and SI = 1050 - 1000
= Tk. 50