General TestA man is twice as fast as a woman. Together the man and the woman do the piece of work in 8 days. In how many days each will do the work if engaged alone?

A man is twice as fast as a woman. Together the man and the woman do the piece of work in 8 days. In how many days each will do the work if engaged alone?

A
man-14days, woman-28 days
B
man-12 days, woman-24 days
C
man-10 days, woman-20days
D
None of these

Solution:

Let the man alone do the work in $x$ days.

Then, the woman alone do the work in $2 x$ days.

Their one day's work $= \frac{1}{8}$ th part of whole work

$i.e. \frac{1}{x} + \frac{1}{2 x} = \frac{1}{8}$

$\Rightarrow x = 12$ days

$∴$ man takes $12$ days and woman $2 x = 24$ days.