| A man is twice as fast as a woman and a woman is twice as fast as a boy in doing a work. If all of them, a man, a woman and a boy can finish the work in 7 days, then how many days a boy will do it alone? |
| [SSC (CGL) Mains 2014] |
A) 49
B) 7
C) 6
D) 42
Correct Answer: A
Solution :
| Let the time taken by boy to complete the work\[=4x\]day |
| Similarly, the time taken by woman to complete the work \[=2x\]days |
| The time taken by man to complete the works \[=x\]days |
| [\[\because \]a woman is twice efficient than a boy and a man is twice efficient than woman] |
| Now, together they can complete the work in 7 days. |
| \[\therefore \]One day's work of all working together |
| \[\frac{1}{4x}+\frac{1}{2x}+\frac{1}{x}=\frac{1}{7}\]\[\Rightarrow \]\[\frac{1+2+4}{4x}=\frac{1}{7}\] |
| \[\Rightarrow \] \[\frac{7}{4x}=\frac{1}{7}\]\[\Rightarrow \]\[x=\frac{49}{4}\] |
| \[\therefore \]A boy can finish the work \[=4x\] |
| \[=4\times \frac{49}{4}=49\,\,\text{days}\] |
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