| If \[\frac{a}{1-a}+\frac{b}{1-b}+\frac{c}{1-c}=1,\]then the value of \[\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}\] [SSC (10+2) 2011] |
A) 1
B) 2
C) 3
D) 4
Correct Answer: D
Solution :
| Given, \[\frac{a}{1-a}+\frac{b}{1-b}+\frac{c}{1-c}=1\] (i) |
| On adding 3 in Eq, (i) on both sides, we get |
| \[\left( \frac{a}{1-a}+1 \right)+\left( \frac{b}{1-b}+1 \right)+\left( \frac{c}{1-c}+1 \right)=3+1=4\] |
| \[\Rightarrow \] \[\frac{a+1-a}{1-a}+\frac{b+1-b}{1-b}+\frac{c+1-c}{1-c}=4\] |
| \[\therefore \] \[\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}=4\] |
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