Barbara DavidBarbara and David can finish a piece of work in ^@ | Math Question and Answer

Answer:

$13$ days

Step by Step Explanation:

10 = rem
m = 10
n = 5
Barbara takes $10$ days to finish the work. So in $1$ day, she finishes $\dfrac { 1 }{ 10 }$ of the work.
David takes $20$ days to finish the work. So in $1$ day, he finishes $\dfrac { 1 }{ 20 }$ of the work.
Since the work is done on alternate days, so the work done in two days $= \dfrac{ 1 }{ 10 } + \dfrac{ 1 } { 20 } = \dfrac{ 2 + 1 }{ 20 } = \dfrac{ 3 }{ 20 }$
Multiply $\dfrac{ 3 }{ 20 }$ by number such that it is less than or equal to $1.$
The work done in $12$ days $= 6 \times \dfrac{ 3 }{ 20 } = \dfrac { 9 }{ 10 }$
Remaining work $= 1 - \dfrac { 9 }{ 10 } = \dfrac { 1 }{ 10 }$
Since, they work in alternate days, on $13^{th}$ day remaining work $\dfrac { 1 }{ 10 }$ is done by Barbara.
Thus, they will take $13$ days to finish the work.

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