A) Rs. 800
B) Rs. 992
C) Rs. 750
D) Rs. 900
Correct Answer: A
$ \Rightarrow $ $ (944-x)=\frac{x\times R\times 3}{100} $
$ \Rightarrow $ $ \frac{100(944-x)}{3x}=R $ (i) Case II $ P=Rs.x, $ $ T=5yr, $ $ R= R $ % $ SI=Rs.(1040-x) $
$ \therefore $ $ SI=\frac{P\times R\times T}{100} $
$ \Rightarrow $ $ (1040-x)=\frac{x\times R\times 5}{100} $
$ \Rightarrow $ $ R=\frac{(1040-x)\times 100}{5x} $ … (ii) From Eqs. (i) and (ii), we get $ \frac{(1040-x)\times 100}{5x}=\frac{100(944-x)}{3x} $
$ \Rightarrow $ $ 3(1040-x)=5(944-x) $
$ \Rightarrow $ $ 3120-3x=4720-5x $
$ \Rightarrow $ $ 2x=4720-3120 $
$ \Rightarrow $ $ 2x=1600 $
$ \Rightarrow $ $ x=Rs.800 $
Alternate Method
Let the principal be Rs. x.
Rate of interest = R%
Case I
Here, $ P=x, $ $ T=2yr $ and $ SI=(880-x) $
$ SI=\frac{P\times R\times T}{100} $
$ \Rightarrow $ $ (880-x)=\frac{x\times R\times 2}{100} $
$ \Rightarrow $ $ R=\frac{100(880-x)}{2x} $ (i) Case II Similarly, $ R=\frac{100(920-x)}{3x} $ From Eqs. (i) and (ii), we get $ \frac{100(880-x)}{2x}=\frac{100(920-x)}{3x} $
$ \Rightarrow $ $ 2640-3x=1840-2x $
$ \Rightarrow $ $ x=800 $
BETA
