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Question

X can do a piece of work in 25 days and Y can finish it in 20 days. They work together for 5 days and then X leaves. In how many days will Y finish the remaining work ?


Solution

Let the total work be $$1$$
Then, According to question X takes 25 days to do 1 work.
Then work done by X in 1 day=$$\dfrac{1}{25}$$

Also according to question Y takes 20 days to do 1 work.
Then work doe by Y in 1 day=$$\dfrac{1}{20}$$

Then total work done by both of them in 1 day $$=\dfrac{1}{20}+\dfrac{1}{25}=\dfrac{9}{100}$$
Then total work done by both of them 5 days$$=\dfrac{45}{100}$$
Then total work left $$=1-\dfrac{45}{100}=\dfrac{55}{100}$$
Now, As Y can do 1 work in 25 days therefore,
Y can do $$\dfrac{55}{100}$$ work in $$\dfrac{55}{100}\times{25}$$ days
$$=\dfrac{55}{4}$$ days

Mathematics

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