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Two-persons-X-and-Y-together-can-do-a-job-in-36-days-If-X-s-ability-to-do-the-work-is-twice-that-of-Y-then-find-the-number-of-days-in-which-Y-can-do-the-work-individually-

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Question Number 9620 by asma last updated on 21/Dec/16
Two persons X and Y together can do a job in 36 days. If X′s ability to do the work is twice that of Y, then find the number of days in which Y can do the work individually.
$$\mathrm{Two}\:\mathrm{persons}\:\mathrm{X}\:\mathrm{and}\:\mathrm{Y}\:\mathrm{together}\:\mathrm{can}\:\mathrm{do}\:\mathrm{a} \\ $$$$\mathrm{job}\:\mathrm{in}\:\mathrm{36}\:\mathrm{days}.\:\mathrm{If}\:\mathrm{X}'\mathrm{s}\:\mathrm{ability}\:\mathrm{to}\:\mathrm{do}\:\mathrm{the} \\ $$$$\mathrm{work}\:\mathrm{is}\:\mathrm{twice}\:\mathrm{that}\:\mathrm{of}\:\mathrm{Y},\:\mathrm{then}\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{days}\:\mathrm{in}\:\mathrm{which}\:\mathrm{Y}\:\mathrm{can} \\ $$$$\mathrm{do}\:\mathrm{the}\:\mathrm{work}\:\mathrm{individually}. \\ $$
Answered by sandy_suhendra last updated on 21/Dec/16
X can do the job in x days Y can do the job in 2x days X and Y in 1 day can do =(1/x)+(1/(2x))=(3/(2x)) part of job so (3/(2x))=(1/(36)) 2x=108 ⇒ x=54 X can do the job in 54 days Y can do the job in 108 days
$$\mathrm{X}\:\mathrm{can}\:\mathrm{do}\:\mathrm{the}\:\mathrm{job}\:\mathrm{in}\:\mathrm{x}\:\mathrm{days} \\ $$$$\mathrm{Y}\:\mathrm{can}\:\mathrm{do}\:\mathrm{the}\:\mathrm{job}\:\mathrm{in}\:\mathrm{2x}\:\mathrm{days} \\ $$$$\mathrm{X}\:\mathrm{and}\:\mathrm{Y}\:\mathrm{in}\:\mathrm{1}\:\mathrm{day}\:\mathrm{can}\:\mathrm{do}\:=\frac{\mathrm{1}}{\mathrm{x}}+\frac{\mathrm{1}}{\mathrm{2x}}=\frac{\mathrm{3}}{\mathrm{2x}}\:\mathrm{part}\:\mathrm{of}\:\mathrm{job} \\ $$$$\mathrm{so}\:\frac{\mathrm{3}}{\mathrm{2x}}=\frac{\mathrm{1}}{\mathrm{36}} \\ $$$$\:\:\:\:\:\mathrm{2x}=\mathrm{108}\:\Rightarrow\:\mathrm{x}=\mathrm{54} \\ $$$$\mathrm{X}\:\mathrm{can}\:\mathrm{do}\:\mathrm{the}\:\mathrm{job}\:\mathrm{in}\:\mathrm{54}\:\mathrm{days} \\ $$$$\mathrm{Y}\:\mathrm{can}\:\mathrm{do}\:\mathrm{the}\:\mathrm{job}\:\mathrm{in}\:\mathrm{108}\:\mathrm{days} \\ $$
Answered by mrW last updated on 21/Dec/16
Y alone needs: ((36)/1)×(1+2)=108 days X alone needs: ((36)/2)×(1+2)=54 days
$$\mathrm{Y}\:\mathrm{alone}\:\mathrm{needs}:\:\frac{\mathrm{36}}{\mathrm{1}}×\left(\mathrm{1}+\mathrm{2}\right)=\mathrm{108}\:\mathrm{days} \\ $$$$\mathrm{X}\:\mathrm{alone}\:\mathrm{needs}:\:\frac{\mathrm{36}}{\mathrm{2}}×\left(\mathrm{1}+\mathrm{2}\right)=\mathrm{54}\:\mathrm{days} \\ $$

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