Question

X and Y together to a certain piece of work in 8 days . if x does it alone he completes the work in 12 days . in how many days will Y alone complete the work ?​

Answer 1

$\huge\textbf{Answer}$

X and Y together do a certain piece of work in 8 days.

Work done by both (X and Y) in 1 day = $\dfrac{1}{8}$ days

If X along complete the work in 12 days.

Then work done by X in 1 day = $\dfrac{1}{12}$ days.

Now we have to find the work done by Y alone.

Work done by XY = Work done by X + Work done by Y

Work done by Y = Work done by XY - Work done by X

Work done by Y = $\dfrac{1}{8}$ - $\dfrac{1}{12}$

= $\dfrac{3\:-\:2}{24}$

= $\dfrac{1}{24}$ days

$\textbf{Work done by Y alone is 24 days.}$

Answer 2

X and Y together do a certain piece of work in 8 days.

Work done by both (X and Y) in 1 day = \dfrac{1}{8}

8

1

days

If X along complete the work in 12 days.

Then work done by X in 1 day = \dfrac{1}{12}

12

1

days.

Now we have to find the work done by Y alone.

Work done by XY = Work done by X + Work done by Y

Work done by Y = Work done by XY - Work done by X

Work done by Y = \dfrac{1}{8}

8

1

- \dfrac{1}{12}

12

1

= \dfrac{3\:-\:2}{24}

24

3−2

= \dfrac{1}{24}

24

1

days

\textbf{Work done by Y alone is 24 days.}Work done by Y alone is 24 days.