Question

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:

• A. (A), (B), (C), (D)
• B. (B), (A), (D), (C)
• C. (B), (A), (C), (D)
• D. (D), (A), (C), (B)

Hint:

For quick mental estimation, you can look at the product of R and T (interest for the whole period) or P and R. For (D), \(5000 \times 12% = 600\) per year, so 1200 for 2 years. For (A), \(6600 \times 5% = 330\) per year, so 660 for 2 years. This quick check shows that D is much larger than A, helping you eliminate incorrect options early.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The question requires calculating the Simple Interest (SI) for four different cases and then arranging the amounts in descending order (largest to smallest).
Step 2: Key Formula or Approach:
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
where P is the Principal amount, R is the Rate of interest per annum, and T is the Time in years.
Step 3: Detailed Explanation:
Let's calculate the SI for each case:
Case (A): P = 6600, R = 5, T = 2
\[ SI_A = \frac{6600 \times 5 \times 2}{100} = 66 \times 10 = \text{Rs. } 660 \]
Case (B): P = 200, R = 6, T = 5
\[ SI_B = \frac{200 \times 6 \times 5}{100} = 2 \times 30 = \text{Rs. } 60 \]
Case (C): P = 840, R = 5, T = 4
\[ SI_C = \frac{840 \times 5 \times 4}{100} = \frac{840 \times 20}{100} = 84 \times 2 = \text{Rs. } 168 \]
Case (D): P = 5000, R = 12, T = 2
\[ SI_D = \frac{5000 \times 12 \times 2}{100} = 50 \times 24 = \text{Rs. } 1200 \]
Now, we compare the SI values:
\(SI_D = 1200\)
\(SI_A = 660\)
\(SI_C = 168\)
\(SI_B = 60\)
The decreasing order is \(1200>660>168>60\), which corresponds to (D) > (A) > (C) > (B).
Step 4: Final Answer:
The correct decreasing order of the simple interests is (D), (A), (C), (B).