Raj can do a piece of work in 15 days and Ram in 20 days . With the help of John , the work gets finished in 5 days . How long will John take to finish the work alone
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Raj can do a piece of work in 15 days and Ram in 20 days . With the help of John , the work gets finished in 5 days . How long will John take to finish the work alone
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Verified answer
Answer:
The number days John takes to finish the work alone is 12 .
Step-by-step explanation:
Given as :
Raj can do a piece of work in 15 days
So, Raj 1 day work = [tex]\dfrac{1}{15}[/tex]
Ram can do a piece of work in 20 days.
So, Ram 1 day work = [tex]\dfrac{1}{20}[/tex]
With the help of John , the work is completed in 5 days
Let john 1 day work = [tex]\dfrac{1}{d}[/tex]
According to question
Raj 1 day work + Ram 1 day work + john 1 day work = total days to finish work
i.e [tex]\dfrac{1}{15}[/tex] + [tex]\dfrac{1}{20}[/tex] + [tex]\dfrac{1}{d}[/tex] = [tex]\dfrac{1}{5}[/tex]
Or, [tex]\dfrac{1}{d}[/tex] = [tex]\dfrac{1}{5}[/tex] - ( [tex]\dfrac{1}{15}[/tex] + [tex]\dfrac{1}{20}[/tex] )
Or, [tex]\dfrac{1}{d}[/tex] = [tex]\dfrac{1}{5}[/tex] - ( [tex]\dfrac{4+3}{60}[/tex] )
Or, [tex]\dfrac{1}{d}[/tex] = [tex]\dfrac{1}{5}[/tex] - [tex]\dfrac{7}{60}[/tex]
Or, [tex]\dfrac{1}{d}[/tex] = [tex]\dfrac{12-7}{60}[/tex]
Or, [tex]\dfrac{1}{d}[/tex] = [tex]\dfrac{5}{60}[/tex]
Or, [tex]\dfrac{1}{d}[/tex] = [tex]\dfrac{1}{12}[/tex]
∴ d = 12
So, The number days John takes to finish the work alone = d = 12
Hence, The number days John takes to finish the work alone is 12 . Answer