Question

Mohan has some money (₹M) that he divides in the ratio of 1:2. He then deposits the smaller amount in a savings scheme that offers a certain rate of interest, and the larger amount in another savings scheme that offers half of that rate of interest. Both interests compound yearly. At the end of two years, the total interest earned from the two savings schemes is ₹830. It is known that one of the interest rates is 10% and that Mohan deposited more than ₹1000 in each saving scheme at the start. What is the value of M?

• A. 7500
• B. 6000
• C. To solve this, the other interest rate must also be given.
• D. 4500
• E. 12000

Answer 1

The Correct Option is B

Step 1: Split the money 

Mohan divides ₹M in the ratio \(1:2\). So, the smaller part = \(\dfrac{M}{3}\) and the larger part = \(\dfrac{2M}{3}\).

Step 2: Assign interest rates

Suppose the smaller part is deposited at rate \(r\). Then the larger part is deposited at rate \(\dfrac{r}{2}\). It is given that one of the rates is \(10\%\). So possibilities are:

• Case 1: \(r = 10\%\) and larger part at \(5\%\).
• Case 2: \(r = 20\%\) and larger part at \(10\%\).

Step 3: Write compound interest formula

For amount \(P\) at rate \(R\%\) compounded yearly for \(2\) years: \[ \text{CI} = P \left(1 + \frac{R}{100}\right)^2 - P \]

Step 4: Check Case 1

Smaller deposit = \(\dfrac{M}{3}\) at \(10\%\). \[ \text{CI}_1 = \frac{M}{3}\left[(1.1)^2 - 1\right] = \frac{M}{3}(0.21) = 0.07M \] Larger deposit = \(\dfrac{2M}{3}\) at \(5\%\). \[ \text{CI}_2 = \frac{2M}{3}\left[(1.05)^2 - 1\right] = \frac{2M}{3}(0.1025) \approx 0.06833M \] Total interest = \(0.07M + 0.06833M = 0.13833M\).

Given total interest = 830. \[ 0.13833M = 830 \quad \Rightarrow \quad M \approx 6000 \]

Step 5: Verify deposits

Smaller deposit = \(\dfrac{6000}{3} = 2000 > 1000\). Larger deposit = \(\dfrac{2 \times 6000}{3} = 4000 > 1000\). ✅ Hence valid.

Step 6: Case 2 check (for completeness)

If smaller deposit = \(\dfrac{M}{3}\) at \(20\%\) and larger = \(\dfrac{2M}{3}\) at \(10\%\), then total interest turns out much larger than 830, so this case is invalid.

Final Answer:

\[ \boxed{M = 6000} \]