John took a loan of Rs. 1500 with simple interest for as many years as the…
2023
John took a loan of Rs. 1500 with simple interest for as many years as the rate of interest. If he paid Rs. 540 as interest at the end of loan period, what was the rate of interest?
- A.
2 %
- B.
5 %
- C.
3 %
- D.
6 %
Attempted by 13 students.
Show answer & explanation
Correct answer: D
Step-by-Step Solution
To find the rate of interest when the time period in years is numerically equal to the rate percentage, we use the standard simple interest formula and substitute the variables.
Define the variables based on the problem:
Principal (P) = Rs. 1500
Simple Interest (S.I.) = Rs. 540
Let the Rate of interest be R%.
According to the problem, the Time (T) = R years.
Apply the simple interest formula:
S.I. = (P * R * T) / 100
Substitute the known values: 540 = (1500 * R * R) / 100
Solve for R:
Simplify the equation: 540 = 15 * R^2
Divide both sides by 15: R^2 = 540 / 15
R^2 = 36
Take the square root of both sides: R = 6