Question: When a bank reduced the rate of interest from $ 6\frac{1}{2} $ %per annum to $ 5\frac{1}{2} $ %per annum, a depositor withdraw Rs. 600 and there by his interest reduced by Rs. 73. Find the initial deposit.
Options:
A) Rs. 4000
B) Rs. 6000
C) Rs. 7000
D) Rs. 9000
Show Answer
Answer:
Correct Answer: A
Solution:
- Initially let $ P=Rs\text{. }x $
Rate $ (R)=\frac{13}{2} $ %per annum and Time (T) = 1 yr
Now, deposit $ =Rs\text{. (}x-\text{600)} $
Rate(R) = $ \frac{11}{2} $ %(T) =1yr
Initial simple interest $ (SI)=\frac{P\times R\times T}{100}=\frac{x\times \frac{13}{2}\times 1}{100}=\frac{13x}{200} $
New simple interest $ (SI)=\frac{(x-600)\times \frac{11}{2}\times 1}{100} $
$ =\frac{11(x-600)}{200} $
According to the question,
$ \frac{13x}{200}-\frac{11(x-600)}{200}=73 $
$ \Rightarrow $ $ 13x-11(x-600)=200\times 73 $
$ \Rightarrow $ $ 2x=200\times 73-600\times 11 $
$ \Rightarrow $ $ 2x=14600-6600 $
$ \Rightarrow $ $ x=4000 $
Hence, initial investment is Rs. 4000.
BETA
