A certain sum becomes 3-fold at 4% annual rate of interest. At what rate, will it become 6-fold?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10%
The question is worked with simple interest, where the interest is \(\frac{P\times R\times T}{100}\). A sum that becomes 3-fold has earned interest equal to twice the principal; the time is found from the first case and used again in the second.
3-fold: interest \(=3P-P=2P\), so \(\displaystyle 2P=\frac{P\times4\times T}{100}\), giving \(T=50\) years
6-fold: interest \(=6P-P=5P\) in the same 50 years
\(\displaystyle 5P=\frac{P\times R\times50}{100}\), so \(R=10\%\)
Shortcut: For a fixed time, simple interest is proportional to the rate.
Interest \(2P\) comes at 4%, and interest \(5P\) is needed in the same time
Rate \(\displaystyle =4\times\frac{5}{2}=10\%\)