Question

Raksha can complete a piece of work in 12 day while Esther takes 20 days to complete the work .They start working together but Raksha leaves 4 days before the work get over . For how many days does Esther work?

Answer 1

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Answer 2

Answer:

Esther work for 10 days

Step-by-step explanation:

Raksha can do a piece of work in 12 days

$\text{Raksha's one day work is = }\frac{1}{12}$

Esther can do a piece of work in 20 days

$\text{Esthers's one day work is = }\frac{1}{20}\\\\\text{Raksha and Esther both together work for one day = }\frac{1}{12}+\frac{1}{20}=\frac{2}{15}$

Let total work completed in x days  

Both work for (x - 4) and Esther work alone for 4 days  

$\text{Both work for (x - 4) days = }(x - 4)\times \frac{2}{15}=\frac{2\cdot x-8}{15}\\\\\text{Esther alone three days work = }4\times \frac{1}{20}=\frac{1}{5}$  

As per give conditions  :

$\frac{1}{5}+ \frac{2\cdot x-8}{15} =1\\\\\text{By LCM solving we will get : }\\\\\implies\frac{3+2\cdot x-8}{15}=1\\\\\implies 2\cdot x-5=15\\\\\implies x = 10$

So, Esther work for 10 days