A) Rs. 10400
B) Rs. 16000
C) Rs. 25600
D) Rs. 31200
Correct Answer: B
Solution :
| [b] 1 yr before, let A's salary be Rs. \[{{x}_{1}}\] and B's salary Rs. \[{{y}_{1}}.\] At present, let A's salary be Rs. \[{{x}_{2}}\] and B's salary be Rs. \[{{y}_{2}}.\] Then, \[\frac{{{x}_{1}}}{{{y}_{1}}}=\frac{3}{4},\]\[\frac{{{x}_{1}}}{{{x}_{2}}}=\frac{4}{5},\]\[\frac{{{y}_{1}}}{{{y}_{2}}}=\frac{2}{3}\] and \[{{x}_{2}}+{{y}_{2}}=41600\] \[\therefore \] \[\frac{{{x}_{1}}}{{{y}_{1}}}\times \frac{{{x}_{2}}}{{{x}_{1}}}\times \frac{{{y}_{1}}}{{{y}_{2}}}=\frac{3}{4}\times \frac{5}{4}\times \frac{2}{3}\] \[\Rightarrow \] \[\frac{{{x}_{2}}}{{{y}_{2}}}=\frac{5}{8}\]\[\Rightarrow \]\[{{y}_{2}}=\frac{8}{5}{{x}_{2}}\] \[\therefore \] \[{{x}_{2}}+\frac{8}{5}{{x}_{2}}=41600\] \[\Rightarrow \] \[\frac{13}{5}{{x}_{2}}=41600\] \[\Rightarrow \] \[{{x}_{2}}=\left( 41600\times \frac{5}{13} \right)=16000\] Hence, A's present salary is Rs. 16000. |
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