Question

A man invested Rs 6000 in a bank with si of 20% per annum . Another amount at 10% per annum . Total si for the whole sum after 4 years is 16% per annum find the total amount of investment ?

• A. 12000
• B. 10000
• C. 32000
• D. 18000

Answer 1

Answer:

B. 10000

Understanding Simple Interest (SI)

• The fundamental formula for Simple Interest is SI = (P × R × T) / 100, where P is the Principal amount, R is the Annual Rate of Interest, and T is the Time in years.
• For competitive exams, it's crucial to understand that Simple Interest accrues only on the initial principal amount, not on accumulated interest.

Applying the Alligation Method for Rates

• The Alligation method is an extremely effective technique for solving problems that involve mixing two or more items with different properties to obtain a mixture with an average property. In this context, we are blending two investments with different annual interest rates to achieve an overall average annual rate.
• This method simplifies complex weighted average calculations, which are common in competitive exams.

Steps for Alligation

1. Place the individual annual interest rates at the top corners:
• Rate 1 (Higher): 20%
• Rate 2 (Lower): 10%
2. Place the overall average annual interest rate in the center:
• Average Rate: 16%
3. Draw diagonal lines and subtract the smaller value from the larger value along these diagonals, placing the results at the bottom corners. These differences represent the inverse ratio of the quantities (principal amounts) associated with each rate.
• Difference 1 (for 10% rate): |16% - 10%| = 6%
• Difference 2 (for 20% rate): |20% - 16%| = 4%
4. The ratio of the principal amounts (P1 : P2) is given by these differences, i.e., the principal associated with Rate 1 (20%) corresponds to Difference 1 (6%), and the principal associated with Rate 2 (10%) corresponds to Difference 2 (4%).
• Therefore, the ratio of Principal 1 (P1, at 20%) to Principal 2 (P2, at 10%) is P1 : P2 = 6 : 4.
• Simplifying this ratio, we get P1 : P2 = 3 : 2.

Calculating the Unknown Investment

• We are given that the first investment (P1) is Rs 6000.
• From the ratio P1 : P2 = 3 : 2, if 3 units correspond to Rs 6000:
• 1 unit = Rs 6000 / 3 = Rs 2000.
• The second investment (P2) corresponds to 2 units:
• P2 = 2 × Rs 2000 = Rs 4000.

Finding the Total Investment

• The total amount of investment is the sum of the first and second investments.
• Total Investment = P1 + P2 = Rs 6000 + Rs 4000 = Rs 10000.