A) \[2000,5%\]
B) \[3000,4%.\]
C) \[2500,5%\]
D) \[~2500,4%\]
Correct Answer: D
Solution :
Let the principal = P and rate = r \[\therefore \] SI after 2 years \[\frac{P\times r\times 2}{100}=\frac{P\times r}{50}\] \[\therefore \] Amount \[=P+\frac{P\times r}{50}=2700\] \[\therefore \,\,\,\,\frac{\Pr }{50}=2700-P\] \[\therefore \,\,\,\,\Pr =50\,(2700-p)\] ?..(i) SI after 4 years \[=\frac{P\times r\times 4}{100}=\frac{\Pr }{25}\] \[\therefore \] Amount- \[P+\frac{\Pr }{25}=2900\] \[\therefore \,\,\,\,\frac{\Pr }{25}=2900-P\] \[\Rightarrow \,\,\,\Pr =25\,(2900-P)\] ?..(ii) Comparing equation (i) and (ii)- \[50(2700-P)=25(2900-P)\] \[2(2700-P)\,=2900-P\] \[5400-2P=2900-P\] \[5400-2900=-P+2P\Rightarrow \underline{\mathbf{P=2500}}\] \[\therefore \] Rate \[=\frac{SI\times 100}{P\times t}\] SI \[=2700-2500=200\] \[\therefore \] Rate \[=\frac{200\times 100}{2500\times 2}=\underline{\mathbf{4%}}\]
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