A) \[1\frac{1}{3}\text{h}\]
B) \[2\,\,\text{h}\]
C) \[1\frac{2}{3}\,\,\text{h}\]
D) \[2\frac{2}{3}\,\,\text{h}\]
Correct Answer: A
Solution :
Let the time taken by A be x hours. |
Then, time taken by B =\[\left( x-\frac{20}{60} \right)\text{h}=\left( x-\frac{1}{3} \right)\text{h}\] |
Ratio of speeds = Inverse ratio of time taken |
\[\therefore \] \[3:4=\left( x-\frac{1}{3} \right):x\] |
\[\Rightarrow \] \[\frac{3x-1}{3x}=\frac{3}{4}\] |
\[\Rightarrow \] \[12x-4=9x\] |
\[\Rightarrow \] \[3x=4\]\[\Rightarrow \]\[x=\frac{4}{3}\text{h}=1\frac{1}{3}\text{h}\] |
Required time \[=1\frac{1}{3}\text{h}\] |
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