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: The ratio of milk and water in a solution is 7 : 4. After adding 8 liters of water, the ratio of milk and water becomes 3 : 2. Find the final amount of water in the solution.

Solution:
Let the initial amount of milk = 7x liters
Let the initial amount of water = 4x liters

According to the question,
7x/(4x + 8) = 3/2
⇒ 2 × 7x = 3 × (4x + 8)
⇒ 14x = 12x + 24
⇒ 14x - 12x = 24
⇒ 2x = 24
⇒ x = 12

∴ Final amount of water = 4x + 8
= 4 × 12 + 8
= 48 + 8 = 56 liters

Question: A man bought some sugar and salt for Tk. 440. The ratio of the weights of sugar and salt is 5 : 2, and the price per unit weight of sugar and salt is in the ratio 6 : 7. What is the price of the total sugar?

Solution:
Given,
Weight ratio (Sugar : Salt) = 5 : 2
Price ratio per unit weight (Sugar : Salt) = 6 : 7

Total price ratio of sugar and salt = (Weight × Price per unit)
= 5 × 6 : 2 × 7
= 30 : 14
= 15 : 7

Total units = 15 + 7 = 22 units

Accordint to the question,
22 units = Tk. 440
⇒ 1 unit = 440/22
∴ 1 unit= Tk. 20

∴ Price of total sugar = 15 × 20 = Tk. 300