Question

Sita takes twice as much time as Gita to complete a work and Rita does it in the same time as Sita and Gita together if all three working together can finish the work in 6 days then the time taken by each of them to finish the work is​

Answer 1

Answer:

Step-by-step explanation:

Let Say Gita  Complete a work  in   G Days

Sita will complete work in 2G days

Gita's 1 day work = 1/G

Sita's 1 day work = 1/2G

Sita + Gita together 1 day work  =  1/G + 1/2G   = 3/2G

Rita 1 day work  = 3/2G

Rita complete work in 2G/3 Days

Sita + Gita + Rita together 1 day work   =  1/G  + 1/2G  + 3/2G  = 3/G

Sita + Gita + Rita together will complete work in  G/3  days

G/3 = 6

=> G = 18 Days

Gita complete work in 18 Days

Sita Complete work in 2*18 = 36 Days

Rita complete work in  2*18/3  = 12 Days

Answer 2

Sita = 36 days

Gita = 18 days

Rita = 12 days

To find:

Sita = ?

Gita = ?

Rita = ?

Given data:

Sita takes twice as much time as Gita to complete a work i.e., s = 2g

Rita does it in the same time as Sita and Gita together i.e., r = s + g

all three working together can finish the work i.e., s + g + r = 6

Solution:

let the value g = 3x

and so          s = 6x

then the value of r will be

                    r = $\frac{1}{6} + \frac{1}{3}$

                      = $\frac{1 + 2}{6}$

                    r = $\frac{1}{2}$ or 2x

all three working together can finish the work i.e.,

                 s + g + r = 6

                $\frac{1}{6x} + \frac{1}{3x} + \frac{1}{2x} = \frac{1}{6}$

in the above given equation substitute x value starting from 1

then by substituting x = 6 we get,

           $\frac{1}{6}$ = $\frac{1}{6 X 6} + \frac{1}{3 X 6} + \frac{1}{2 X 6}$

           $\frac{1}{6}$ = $\frac{1}{36} + \frac{1}{18} + \frac{1}{12}$

taking LCM we get

          $\frac{1}{6}$ = $\frac{2 + 4 + 6}{72}$    

          $\frac{1}{6}$ = $\frac{12}{72}$

          $\frac{1}{6}$ = $\frac{1}{6}$    

thus LHS = RHS

then Sita = 36 days

       Gita = 18 days

       Rita = 12 days

To solve more:

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2. A can do a piece of work in 20 days and b can do it in 25 days .both of them finished the work and earned rs.3600.then a's share is?

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