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, 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. 

Answer 2

We have \(\frac{5.5\times 8000}{100}+\frac{5.6\times 5000}{100}+\frac{x\times 7000}{100}=\frac{5}{100}\times 20000\)
\(⇒440+280+70x=1000\)
\(x=4\%\)
Now interest \(=\frac{20000\times 4}{100}=Rs\ 800\)