Question : The rate of interest per annum at which the total simple interest of a certain capital for 1 year is equal to the total simple interest of the same capital at the rate of 5% per annum for 2 years, is:
Option 1: $\frac{5}{2}$%
Option 2: $10$%
Option 3: $25$%
Option 4: $12.5$%
Correct Answer: $10$%
Solution :
Given: R = R% in the first case and 5% in the second case.
T = 1 year for the first case and 2 years for the second case.
Let P be the capital, which is equal in both cases.
We know that,
Simple Interest = $\frac{\text{Principle×Rate×Time}}{100}$
When simple interest is the same, then,
$\frac{\text{P×R×1}}{100}$ = $\frac{\text{P×5×2}}{100}$
$\therefore$ R = 10%
Hence, the correct answer is $10$%.
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