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

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. \[ \boxed{\text{Rs. } 2654.24 \Rightarrow \text{None of the above}} \]