Question:medium

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

Updated On: Jan 15, 2026

  • 900

  • 700

  • 1000

  • 800

Show Solution

The Correct Option is D

Solution and Explanation

Nitu's initial capital is ₹20,000. She allocates her funds as follows:

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

The total annual interest earned across all investments is ₹1,000, equivalent to 5% of her initial ₹20,000. Determine the interest rate \( x \) for Bank C and calculate the interest Nitu would earn if the entire ₹20,000 were invested in Bank C at this rate.

Step 1: Calculate Interest from Bank A

The interest earned from Bank A is calculated as:

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

Step 2: Calculate Interest from Bank B

The interest earned from Bank B is calculated as:

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

Step 3: Calculate Interest from Bank C

First, determine the principal amount invested in Bank C:

Remaining principal: \[ P = 20000 - (8000 + 5000) = ₹7000 \]

The interest earned from Bank C is:

\[ \text{Interest from Bank C} = \frac{7000 \times x}{100} = ₹70x \]

Step 4: Formulate and Solve the Total Interest Equation

The sum of the interest from all three banks equals the total annual interest:

\[ 440 + 280 + 70x = 1000 \]

Simplify the equation:

\[ 720 + 70x = 1000 \]

Isolate the term with \( x \):

\[ 70x = 1000 - 720 \]

\[ 70x = 280 \]

Solve for \( x \):

\[ x = \frac{280}{70} = 4 \]

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

Step 5: Calculate Potential Interest if Entire Amount is Invested in Bank C

If Nitu invested the entire ₹20,000 in Bank C at the determined rate of 4%, the interest earned would be:

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

Final Answer:

If Nitu had invested her entire ₹20,000 in Bank C at a rate of 4%, her annual interest earnings would be: \[ \boxed{₹800} \]

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