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Karanja-and-Ouma-can-do-a-certain-job-in-6-days-Karanja-alone-can-do-the-work-in-5-days-more-than-Ouma-How-many-days-can-Karanja-take-to-do-the-job-alone-




Question Number 72498 by Mr Jor last updated on 29/Oct/19
Karanja and Ouma can do a   certain job in 6 days. Karanja   alone can do the work in 5 days  more than Ouma. How many   days can Karanja take to do the  job alone?
$${Karanja}\:{and}\:{Ouma}\:{can}\:{do}\:{a}\: \\ $$$${certain}\:{job}\:{in}\:\mathrm{6}\:{days}.\:{Karanja}\: \\ $$$${alone}\:{can}\:{do}\:{the}\:{work}\:{in}\:\mathrm{5}\:{days} \\ $$$${more}\:{than}\:{Ouma}.\:{How}\:{many}\: \\ $$$${days}\:{can}\:{Karanja}\:{take}\:{to}\:{do}\:{the} \\ $$$${job}\:{alone}? \\ $$
Answered by Tanmay chaudhury last updated on 29/Oct/19
(K+O) perform  in 1 day (1/6)portion of work  let O completes the  work in x days  so O perform  in 1 days (1/x)portion  let K completes the work in (x+5)days   so K perform the work in 1 days (1/(x+5))portion  (1/x)+(1/(x+5))=(1/6)  ((x+5+x)/(x^2 +5x))=(1/6)→x^2 +5x=12x+30  x^2 −7x−30=0  x^2 −10x+3x−30=0  x(x−10)+3(x−10)=0  (x−10)(x+3)=0  x≠−3   so x=10  so Ouma complete the work in 10 days  and Karanja completd work in 15 days
$$\left({K}+{O}\right)\:{perform}\:\:{in}\:\mathrm{1}\:{day}\:\frac{\mathrm{1}}{\mathrm{6}}{portion}\:{of}\:{work} \\ $$$${let}\:{O}\:{completes}\:{the}\:\:{work}\:{in}\:{x}\:{days} \\ $$$${so}\:{O}\:{perform}\:\:{in}\:\mathrm{1}\:{days}\:\frac{\mathrm{1}}{{x}}{portion} \\ $$$${let}\:{K}\:{completes}\:{the}\:{work}\:{in}\:\left({x}+\mathrm{5}\right){days} \\ $$$$\:{so}\:{K}\:{perform}\:{the}\:{work}\:{in}\:\mathrm{1}\:{days}\:\frac{\mathrm{1}}{{x}+\mathrm{5}}{portion} \\ $$$$\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{x}+\mathrm{5}}=\frac{\mathrm{1}}{\mathrm{6}} \\ $$$$\frac{{x}+\mathrm{5}+{x}}{{x}^{\mathrm{2}} +\mathrm{5}{x}}=\frac{\mathrm{1}}{\mathrm{6}}\rightarrow{x}^{\mathrm{2}} +\mathrm{5}{x}=\mathrm{12}{x}+\mathrm{30} \\ $$$${x}^{\mathrm{2}} −\mathrm{7}{x}−\mathrm{30}=\mathrm{0} \\ $$$${x}^{\mathrm{2}} −\mathrm{10}{x}+\mathrm{3}{x}−\mathrm{30}=\mathrm{0} \\ $$$${x}\left({x}−\mathrm{10}\right)+\mathrm{3}\left({x}−\mathrm{10}\right)=\mathrm{0} \\ $$$$\left({x}−\mathrm{10}\right)\left({x}+\mathrm{3}\right)=\mathrm{0} \\ $$$${x}\neq−\mathrm{3}\:\:\:{so}\:{x}=\mathrm{10} \\ $$$${so}\:{Ouma}\:{complete}\:{the}\:{work}\:{in}\:\mathrm{10}\:{days} \\ $$$${and}\:{Karanja}\:{completd}\:{work}\:{in}\:\mathrm{15}\:{days} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$
Commented by malwaan last updated on 30/Oct/19
very nice !
$${very}\:{nice}\:! \\ $$

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