Sita takes twice as much time as Gita to comp | vedclass

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Question

(A) Let Gita take $x$ days to complete the work. Then,Sita takes $2x$ days to complete the same work.Rita takes the same time as Sita and Gita togethe

Vedclass · Accepted Answer

$18, 36,$ and $12$

Vedclass · Answer

(A) Let Gita take $x$ days to complete the work. Then,Sita takes $2x$ days to complete the same work.Rita takes the same time as Sita and Gita together. The time taken by Sita and Gita together is $\frac{x 	imes 2x}{x + 2x} = \frac{2x^2}{3x} = \frac{2x}{3}$ days.So,Rita takes $\frac{2x}{3}$ days to complete the work.When all three work together,the time taken is given by the formula $\frac{1}{T} = \frac{1}{x} + \frac{1}{2x} + \frac{1}{2x/3}$.$\frac{1}{6} = \frac{1}{x} + \frac{1}{2x} + \frac{3}{2x}$.$\frac{1}{6} = \frac{2 + 1 + 3}{2x} = \frac{6}{2x} = \frac{3}{x}$.Therefore,$x = 18$ days.Thus,Gita takes $18$ days,Sita takes $2x = 36$ days,and Rita takes $\frac{2x}{3} = 12$ days.

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 (in days):

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