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

Answer: (D)

800

Answer 2

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, and the remaining amount at x% in bank C.
The combined annual interest income from these investments is equal to 5% of the initial capital,which means the total interest from these investments should be $₹20,000 \times 5\% = ₹1,000$.
Let's calculate the interest from each bank:
Bank A:
Principal (P)=₹8,000
Rate (R)=5.5%
Time (T)=1 year
Interest (I)=$\frac{P \times R \times T}{100} = \frac{₹8,000 \times 5.5 \times 1}{100} = ₹440$
Bank B:
Principal (P)=₹5,000
Rate (R)=5.6%
Time (T)=1 year
Interest (I)=$\frac{P \times R \times T}{100} = \frac{₹5,000 \times 5.6 \times 1}{100} = ₹280$
Bank C:
Principal (P)=₹20,000-(₹8,000+₹5,000) =₹7,000
Rate (R)=x% (unknown)
Time (T)=1 year
Interest (I)=$\frac{P \times R \times T}{100}=\frac{₹7,000 \times x \times 1}{100}=₹70x$
Now,we can set up an equation based on the given information:
₹440+₹280+₹70x=₹1,000
Combine the interest terms:
₹440+₹280=₹720
So,the equation becomes:
₹720+₹70x=₹1,000
Now, solve for x:
₹70x=₹1,000-₹720
₹70x=₹280
x=$\frac{₹280}{₹70}$
x=4
So, Nitu would have invested ₹4,000 in bank C (if she invested the remaining amount there) at a rate of 4%.
Now,let's calculate the interest Nitu would have earned if she had invested her entire initial capital of ₹20,000 in bank C at a rate of 4%:
Interest (I)=$\frac{P \times R \times T}{100}=\frac{₹20,000 \times 4 \times 1}{100}=₹800$
Therefore,if Nitu had invested her entire initial capital in bank C alone, her annual interest income would have been ₹800.