A) \[\frac{1}{a}+\frac{1}{b}=\frac{2}{c}\]
B) \[\frac{1}{a}+\frac{1}{b}=2c\]
C) \[a+b=c\]
D) None of these
Correct Answer: A
Solution :
[a] Let distance AB = x units Let \[\frac{3}{5}x\] distance is covered in \[{{t}_{1}}\] time and \[\frac{2}{5}x\] distance is covered in \[{{t}_{2}}\] time \[\therefore \] \[3a=\frac{\frac{3}{5}x}{{{t}_{1}}}\Rightarrow {{t}_{1}}=\frac{x}{5a}\] ? (1) and \[2b=\frac{\frac{2}{5}x}{{{t}_{2}}}\Rightarrow {{t}_{2}}=\frac{x}{5b}\] ? (2) Total time taken in going from B to A and back at speed of 5c \[t=\frac{2x}{5c}\] Now, \[t={{t}_{1}}+{{t}_{2}}\] \[\therefore \] \[\frac{2x}{5c}=\frac{x}{5a}+\frac{x}{5b}\] \[\Rightarrow \] \[\frac{2}{c}=\frac{1}{a}+\frac{1}{b}\]
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