Question

A man invests a certain amount at 6% per annum simple interest and another amount at 7% per annum simple interest. His income from the interest after 2 years was Rs. 348. The ratio of the first amount to the second is 4:5. Find the total amount invested.

• A. Rs. 2600
• B. Rs. 2900
• C. Rs. 2700
• D. None of the above

Hint:

Write the two amounts as 4k and 5k, add their simple interests for 2 years, and solve for k.

Answer 1

The Correct Option is D

To find the total amount invested, let's denote the amount invested at 6% per annum as \( A_1 \) and the amount invested at 7% per annum as \( A_2 \). According to the problem, the ratio of \( A_1 \) to \( A_2 \) is 4:5.  

Thus, we can express these amounts in terms of a common variable \( x \):

• The amount invested at 6% per annum: \( A_1 = 4x \)
• The amount invested at 7% per annum: \( A_2 = 5x \)

The total interest earned from these investments after 2 years is Rs. 348. 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
• \( T \) is the time in years

Let's calculate the interest from each investment:

• Interest from the first amount invested at 6%: \(SI_1 = \frac{4x \times 6 \times 2}{100} = \frac{48x}{100}\)
• Interest from the second amount invested at 7%: \(SI_2 = \frac{5x \times 7 \times 2}{100} = \frac{70x}{100}\)

Adding these interests, we get the total interest:

\(\frac{48x}{100} + \frac{70x}{100} = 348\)

Combining the terms on the left side gives: \(\frac{118x}{100} = 348\)

Solving for \( x \):

\(118x = 348 \times 100\)

\(118x = 34800\)

Simplifying for \( x \):

\(x = \frac{34800}{118} = 295\)

Therefore, the amounts invested are:

• \( A_1 = 4x = 4 \times 295 = 1180 \)
• \( A_2 = 5x = 5 \times 295 = 1475 \)

The total amount invested is:

\(A_1 + A_2 = 1180 + 1475 = 2655\)

Therefore, none of the provided options match our calculated total investment, confirming that the correct answer is indeed "None of the above."

Answer 2

Step 1: Set up the two invested amounts using the given ratio.
The first amount and the second amount are in the ratio 4:5, so write them as \(4k\) and \(5k\) for some positive number \(k\). Their sum, \(9k\), is the total amount invested.

Step 2: Write the simple interest earned from each part over 2 years.
Interest from the first part = \(\dfrac{4k \times 6 \times 2}{100} = 0.48k\). Interest from the second part = \(\dfrac{5k \times 7 \times 2}{100} = 0.70k\).

Step 3: Add both interests and use the total income to solve for k.
Total interest = \(0.48k + 0.70k = 1.18k\). This equals 348, so \(1.18k = 348\), giving \(k = \dfrac{348}{1.18} = \dfrac{17400}{59} \approx 294.92\).

Step 4: Find the total amount invested and compare with the options.
Total amount = \(9k = 9 \times \dfrac{17400}{59} = \dfrac{156600}{59} \approx 2654.24\). This is not a whole rupee figure and does not match Rs. 2600, Rs. 2900 or Rs. 2700.

Final Answer:
The total amount invested is about Rs. 2654.24, which does not match any of the first three fixed options. \[ \boxed{\text{Rs. } 2654.24 \Rightarrow \text{None of the above}} \]