Manish observes that his ratio of principal amount to amount received

1.	Manish observes that his ratio of principal amount to amount received at a rate of simple interest for a fixed period of time is 2 : 3. After 4 years with the same rate of simple interest his ratio of principal amount to amount obtained is 5 : 8. Find the rate of simple interest.1. 2.5%2. 3%3. 4%4. 3.5%
Answer» Correct Answer - Option 1 : 2.5% Given: P₁: A₁ = 2 : 3 After 4 years = P₁: A₂ = 5 : 8 Formula used: I = PRN / 100 Where P = Principal amount, R = Rate of interest in %, N = Number of years, I = Interest earned Calculation: Here, principal amount remains the same and rate of simple interest also remains same. ⇒ 2 : 3 = 1 (Difference) ⇒ 5 : 8 = 3 (Difference) Now, 2 part and 5 part is principal amount which is same so equating principal amount ⇒ 10 : 15 = 5----(1) ⇒ 10 : 16 = 6 ----(2) Equation 1 shows interest obtained after fixed period of time and equation 2 shows interest obtained after 4 years from interest 1 ⇒ Interest in 4 years = (6 – 5) units ⇒ Interest in 4 years = 1 unit ⇒ Interest in 1 years = 1/4 units Placing it in formula, ⇒ 1 / 4 = 10 × R × 1 / 100 [Let, principal is 10 unit and time is 1year] ⇒ R = 100 / (10 × 4) ⇒ R = 2.5% ∴ The required rate of simple interest is 2.5%.

Manish observes that his ratio of principal amount to amount received at a rate of simple interest for a fixed period of time is 2 : 3. After 4 years with the same rate of simple interest his ratio of principal amount to amount obtained is 5 : 8. Find the rate of simple interest.1. 2.5%2. 3%3. 4%4. 3.5%

Answer» Correct Answer - Option 1 : 2.5%

Given:

P₁: A₁ = 2 : 3

After 4 years = P₁: A₂ = 5 : 8

Formula used:

I = PRN / 100

Where P = Principal amount, R = Rate of interest in %, N = Number of years, I = Interest earned

Calculation:

Here, principal amount remains the same and rate of simple interest also remains same.

⇒ 2 : 3 = 1 (Difference)

⇒ 5 : 8 = 3 (Difference)

Now, 2 part and 5 part is principal amount which is same so equating principal amount

⇒ 10 : 15 = 5----(1)

⇒ 10 : 16 = 6 ----(2)

Equation 1 shows interest obtained after fixed period of time and equation 2 shows interest obtained after 4 years from interest 1

⇒ Interest in 4 years = (6 – 5) units

⇒ Interest in 4 years = 1 unit

⇒ Interest in 1 years = 1/4 units

Placing it in formula,

⇒ 1 / 4 = 10 × R × 1 / 100 [Let, principal is 10 unit and time is 1year]

⇒ R = 100 / (10 × 4)

⇒ R = 2.5%

∴ The required rate of simple interest is 2.5%.