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: Name the two parts directly instead of using a ratio constant.
Let the first amount be $A$ and the second be $B$, with $\dfrac{A}{B} = \dfrac{4}{5}$, so $5A = 4B$, or $B = \dfrac{5A}{4}$.

Step 2: Write the total simple interest equation for 2 years.
Interest from $A$ at 6% for 2 years is $\dfrac{6 \times 2 \times A}{100} = 0.12A$. Interest from $B$ at 7% for 2 years is $\dfrac{7 \times 2 \times B}{100} = 0.14B$. Their sum is 348, so $0.12A + 0.14B = 348$.

Step 3: Substitute B in terms of A and solve.
$0.12A + 0.14\left(\dfrac{5A}{4}\right) = 348$, which is $0.12A + 0.175A = 348$, so $0.295A = 348$, giving $A \approx 1179.66$.

Step 4: Find B and the total, then check the options.
$B = \dfrac{5 \times 1179.66}{4} \approx 1474.58$. Total invested $= A + B \approx 2654.24$, the same figure as before, since this is just a different way of writing the same ratio. This does not equal Rs. 2600, Rs. 2900 or Rs. 2700.

Final Answer:
Total amount invested is about Rs. 2654.24, so the answer is none of the given whole number options. \[ \boxed{\text{None of the given options}} \]