Consider the simple interest of the following
(A) A sum of Rs 200 at 6% per annum for 5 yr.
(B) A sum of Rs 2000 at \(13\frac{1}{2}\)% per annum for 4 yr.
(C) A sum of Rs 2600 at 4% per annum for 5 yr.
(D) A sum of Rs 68000 at \(16\frac{2}{3}\)% per annum for 9 months.
Arrange the above in descending order.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (D), (B), (C), (A)
Simple interest is \(\displaystyle\mathrm{SI}=\frac{P\times R\times T}{100}\), with the time \(T\) in years, so the 9 months of (D) are taken as \(\frac{3}{4}\) of a year. Working out the interest on each sum:
(A) \(\displaystyle\frac{200\times6\times5}{100}=\) Rs 60
(B) \(\displaystyle\frac{2000\times13.5\times4}{100}=\) Rs 1080
(C) \(\displaystyle\frac{2600\times4\times5}{100}=\) Rs 520
(D) \(16\frac{2}{3}\%\) is \(\frac{1}{6}\), so the interest is \(\displaystyle 68000\times\frac{1}{6}\times\frac{3}{4}=\) Rs 8500
From the largest to the smallest: 8500, 1080, 520, 60. The biggest sum, lent for the shortest time, still earns by far the most.