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

$$\mathrm{Two}\mathrm{persons}\mathrm{X}\mathrm{and}\mathrm{Y}\mathrm{together}\mathrm{can}\mathrm{do}\mathrm{a}$$$$\mathrm{job}\mathrm{in}36\mathrm{days}.\mathrm{If}{\mathrm{X}}^{\prime }\mathrm{s}\mathrm{ability}\mathrm{to}\mathrm{do}\mathrm{the}$$$$\mathrm{work}\mathrm{is}\mathrm{twice}\mathrm{that}\mathrm{of}\mathrm{Y},\mathrm{then}\mathrm{find}\mathrm{the}$$$$\mathrm{number}\mathrm{of}\mathrm{days}\mathrm{in}\mathrm{which}\mathrm{Y}\mathrm{can}$$$$\mathrm{do}\mathrm{the}\mathrm{work}\mathrm{individually}.$$

Answered by sandy_suhendra last updated on 21/Dec/16

$$\mathrm{X}\mathrm{can}\mathrm{do}\mathrm{the}\mathrm{job}\mathrm{in}\mathrm{x}\mathrm{days}$$$$\mathrm{Y}\mathrm{can}\mathrm{do}\mathrm{the}\mathrm{job}\mathrm{in}2\mathrm{x}\mathrm{days}$$$$\mathrm{X}\mathrm{and}\mathrm{Y}\mathrm{in}1\mathrm{day}\mathrm{can}\mathrm{do}=\frac{1}{\mathrm{x}}+\frac{1}{2\mathrm{x}}=\frac{3}{2\mathrm{x}}\mathrm{part}\mathrm{of}\mathrm{job}$$$$\mathrm{so}\frac{3}{2\mathrm{x}}=\frac{1}{36}$$$$2\mathrm{x}=108\Rightarrow \mathrm{x}=54$$$$\mathrm{X}\mathrm{can}\mathrm{do}\mathrm{the}\mathrm{job}\mathrm{in}54\mathrm{days}$$$$\mathrm{Y}\mathrm{can}\mathrm{do}\mathrm{the}\mathrm{job}\mathrm{in}108\mathrm{days}$$

Answered by mrW last updated on 21/Dec/16

$$\mathrm{Y}\mathrm{alone}\mathrm{needs}:\frac{36}{1}\times (1+2)=108\mathrm{days}$$$$\mathrm{X}\mathrm{alone}\mathrm{needs}:\frac{36}{2}\times (1+2)=54\mathrm{days}$$

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