Nikita,Nishita,and Kavita can complete a work | vedclass

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(C) Let the work done by Nikita,Nishita,and Kavita be $A, B,$ and $C$ respectively.Given: $(A+B+C)$ can complete the work in $2 \frac{2}{3} = \frac{8}

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$3 \frac{3}{7}$

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(C) Let the work done by Nikita,Nishita,and Kavita be $A, B,$ and $C$ respectively.Given: $(A+B+C)$ can complete the work in $2 \frac{2}{3} = \frac{8}{3}$ days.$(B+C)$ can complete the work in $4$ days.$B$ alone can complete the work in $6$ days.First,find the time taken by $C$ (Kavita) alone:Since $(B+C)$ takes $4$ days and $B$ takes $6$ days,the work done by $C$ in $1$ day is $\frac{1}{4} - \frac{1}{6} = \frac{3-2}{12} = \frac{1}{12}$.So,$C$ alone takes $12$ days.Next,find the time taken by $A$ (Nikita) alone:Since $(A+B+C)$ takes $\frac{8}{3}$ days,their $1$-day work is $\frac{3}{8}$.$A$'s $1$-day work $= \frac{3}{8} - (B+C)$'s $1$-day work $= \frac{3}{8} - \frac{1}{4} = \frac{3-2}{8} = \frac{1}{8}$.So,$A$ alone takes $8$ days.Now,find the time taken by $A$ and $B$ (Nikita and Nishita) together:Their combined $1$-day work $= \frac{1}{8} + \frac{1}{6} = \frac{3+4}{24} = \frac{7}{24}$.Therefore,they can complete the work in $\frac{24}{7} = 3 \frac{3}{7}$ days.

Nikita,Nishita,and Kavita can complete a work in $2 \frac{2}{3}$ days. If Nishita and Kavita can complete it in $4$ days,and Nishita alone can do it in $6$ days,then in how many days can Nikita and Nishita complete the work?

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