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%
1. 2.5%
2. 3%
3. 4%
4. 3.5%
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%.