Question

Nitu has an initial capital of ₹20,000.Out of this,she invests ₹8,000 at \(5.5\%\) in bank A,₹5,000 at \(5.6\%\) in bank B and the remaining amount at \(x\%\) in bank C,each rate being simple interest per annum.Her combined annual interest income from these investments is equal to \(5\%\) of the initial capital. If she had invested her entire initial capital in bank C alone,then her annual interest income,in rupees,would have been

• A. 900
• B. 700
• C. 1000
• D. 800

Answer 1

The Correct Option is D

Nitu has an initial capital of ₹20,000. She invests:

• ₹8,000 at 5.5% in Bank A
• ₹5,000 at 5.6% in Bank B
• The remaining ₹7,000 in Bank C at an unknown rate \( x\% \)

The total annual interest earned is ₹1,000 (which is 5% of ₹20,000). Find the rate \( x \) and the interest she would earn if she invested all ₹20,000 in Bank C at that rate.

Step 1: Interest from Bank A

\[ \text{Interest} = \frac{8000 \times 5.5 \times 1}{100} = ₹440 \]

Step 2: Interest from Bank B

\[ \text{Interest} = \frac{5000 \times 5.6 \times 1}{100} = ₹280 \]

Step 3: Interest from Bank C

Remaining principal: \[ P = 20000 - (8000 + 5000) = ₹7000 \] \[ \text{Interest from Bank C} = \frac{7000 \times x}{100} = ₹70x \]

Step 4: Total Interest Equation

\[ 440 + 280 + 70x = 1000 \Rightarrow 720 + 70x = 1000 \Rightarrow 70x = 280 \Rightarrow x = \frac{280}{70} = 4 \]

So, the interest rate at Bank C is \( \boxed{4\%} \).

Step 5: What if Nitu Invested ₹20,000 Entirely in Bank C?

\[ \text{Interest} = \frac{20000 \times 4}{100} = ₹800 \]

Final Answer:

If Nitu had invested her entire ₹20,000 in Bank C at 4%, she would have earned an annual interest of: \[ \boxed{₹800} \]

Answer 2

Nitu invested ₹8,000 at 5.5%, ₹5,000 at 5.6%, and the remaining ₹7,000 at an unknown rate \( x\% \). The total interest from all investments equals 5% of her total capital ₹20,000.

Step 1: Set Up the Equation

\[ \frac{5.5 \times 8000}{100} + \frac{5.6 \times 5000}{100} + \frac{x \times 7000}{100} = \frac{5}{100} \times 20000 \]

Step 2: Simplify

\[ 440 + 280 + 70x = 1000 \Rightarrow 70x = 280 \Rightarrow x = \frac{280}{70} = 4\% \]

Step 3: Calculate Total Interest if Entire ₹20,000 is Invested at 4%

\[ \text{Interest} = \frac{20000 \times 4}{100} = ₹800 \]

Final Answer:

\[ \boxed{x = 4\%}, \quad \boxed{\text{Interest} = ₹800} \]