Arrange the simple interest of the following cases in decreasing order -

(A) The simple interest on Rs 6600 at 5% per annum for 2 yrs.

(B) The simple interest on Rs 200 at 6% per annum for 5 yrs.

(C) The simple interest on Rs 840 at 5% per annum for 4 yrs.

(D) The simple interest on Rs 5000 at 12% per annum for 2 yrs.

Choose the correct answer from the options given below:

The correct answer is (D), (A), (C), (B).

To find the decreasing order of simple interest for the given cases, we need to calculate the simple interest (SI) for each case individually using the standard formula:
$$SI=\frac{P\times R\times T}{100}$$
where P is the Principal amount, R is the Rate of interest per annum, and T is the Time period in years.

Step 1: Calculate the simple interest for Case (A)
Here, Principal (P) = Rs 6600, Rate (R) = 5%, Time (T) = 2 years.
$$S{I}_A=\frac{6600\times 5\times 2}{100}=66\times 10=\text{Rs }660$$

Step 2: Calculate the simple interest for Case (B)
Here, Principal (P) = Rs 200, Rate (R) = 6%, Time (T) = 5 years.
$$S{I}_B=\frac{200\times 6\times 5}{100}=2\times 30=\text{Rs }60$$

Step 3: Calculate the simple interest for Case (C)
Here, Principal (P) = Rs 840, Rate (R) = 5%, Time (T) = 4 years.
$$S{I}_C=\frac{840\times 5\times 4}{100}=\frac{840\times 20}{100}=84\times 2=\text{Rs }168$$

Step 4: Calculate the simple interest for Case (D)
Here, Principal (P) = Rs 5000, Rate (R) = 12%, Time (T) = 2 years.
$$S{I}_D=\frac{5000\times 12\times 2}{100}=50\times 24=\text{Rs }1200$$

Step 5: Arrange the calculated simple interest values in decreasing order
Comparing the obtained values:
- Case (D) Simple Interest = Rs 1200
- Case (A) Simple Interest = Rs 660
- Case (C) Simple Interest = Rs 168
- Case (B) Simple Interest = Rs 60

Since Rs 1200 > Rs 660 > Rs 168 > Rs 60, the decreasing order is:
(D), (A), (C), (B).