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

Question: How many years will Tk. 1500 need at 4% simple interest to earn the same interest as Tk. 2000 earns in 3 years at 5% simple interest?

Solution:
Interest from Tk. 2000 in 3 years at 5%:
SI = (P × R × T)/100
= (2000 × 5 × 3)/100
= 300 Tk.

Now,
Tk. 1500 to Produce the Same Interest (Tk. 300) at 4%:
Principal, P = Tk. 1500
Interest, SI = Tk. 300
Interest Rate, R = 4%
​ Time, T = ? years

SI = PRT/100
⇒ T = (SI × 100)/(P × R)
⇒ T = (300 × 100)/(1500 × 4)
⇒ T = 30000/6000
∴ T = 5 years

Question: What is the compound amount of Tk. 3200 for 2 years at a rate of interest 5% per annum?

Solution:
Given,
Principal, P = 3200
Rate, r = 5% = 5/100 = 1/20
Time, n = 2 years

We know,
A = P(1 + r)ⁿ
  = 3200 × (1 + 1/20)²
  = 3200 × (21/20)²
  = (3200 × 21 × 21) / (20 × 20)
  = (3200 × 441) / 400
  = 1411200 / 400
  = 3528

∴ The compound amount is Tk. 3528.