Question

A, B and C together can finish a piece of work in 4 days, A alone

can do it in 9 days and B alone in 18 days How many days will be

taken by C to do it alone?



please provide with a clear explanation​

Answer 1

Answer:

A, B and C together can finish a piece of work in 4 days, A alone

can do it in 9 days and B alone in 18 days How many days will be

taken by C to do it alone?

please provide with a clear explanation

Answer 2

 

GIVEN :-

• A , B and C can finish a piece of work in 4 days .

• A alone can do it in 9 days .

• B alone can do it in 18 days .

TO FIND :-

• Number of days taken by C to do it alone .

SOLUTION :-

   Let time taken by C alone to complete the work be x days .

   In one day , C does  $\sf\dfrac{1}{x}$ of the work .

   In one day , A does $\dfrac{1}{9}$ of the work .

   In one day , B does  $\sf\dfrac{1}{18}$ of the work .

   According to the question ,

      $\longrightarrow \sf\dfrac{1}{4}=\dfrac{1}{9}+\dfrac{1}{18}+\dfrac{1}{x} \\\\\longrightarrow \dfrac{1}{x} = \dfrac{1}{4}-\dfrac{1}{9}-\dfrac{1}{18}\\\\\longrightarrow \dfrac{1}{x} = \dfrac{9}{36}-\dfrac{4}{36}-\dfrac{2}{36} \\\\\longrightarrow \dfrac{1}{x} = \dfrac{3}{36}\\\\\longrightarrow 3x=36\\\\\longrightarrow x = 12$

   Number of days taken by C to do the work alone = 12 days .