| 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. |
A) Rs. 4000
B) Rs. 6000
C) Rs. 7000
D) Rs. 9000
Correct Answer: A
Solution :
| Initially let \[P=\text{Rs}\text{. }x\] |
| Rate \[(R)=\frac{13}{2}\]%per annum and Time (T) = 1 yr |
| Now, deposit \[=\text{Rs}\text{. (}x-\text{600)}\] |
| 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. |
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