Question

Q.6.X can do a piece of work in 30 days. Y can do it in 20 days, and Z can do it in 24 days. In how many days will they all do it together?​

Answer 1

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Q.6.X can do a piece of work in 30 days. Y can do it in 20 days, and Z can do it in 24 days. In how many days will they all do it together?

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$\small\tt{Adding\:X\:Y\:and\:Z\:work.}$

$\small\tt{Total\:Time\:=\:X+\:Y+\:Z\:}$

$\small\tt{They\:all\: will \:take \:}\\\\{\small\tt{\frac{1}{30}}+{\frac{1}{20}}+{\frac{1}{24}}}\: =\:{\frac {1}{8}}\rightarrow\:\:</p><p>{8}\\\\{\small\bf{It\: will\:take\:8\:days \:to \:complete}}\\{\small\bf{the\: work}}$

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$\bf\blue{\underline{\boxed{Hope\:</p><p>It\: Help\:You}}}$

Answer 2

Answer :-

• 8 Days

Concept Used :-

• For finding the time taken by them if they work together, we will add the amount of workdone by them within one day and then find the time taken by them .

Explanation :-

• Work by x in one day = $\bf{\dfrac{1}{30}}$

• Work by y in one day = $\bf{\dfrac{1}{20}}$

• Work by z in one day = $\bf{\dfrac{1}{24}}$

A.T.Q

★ We have to find the number of days in which they will complete the work if they all do work together

$\mapsto\sf{\dfrac{1}{Time}\:=\:\dfrac{1}{30}+\dfrac{1}{20}+\dfrac{1}{24}}$

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$\mapsto\sf{\dfrac{1}{Time}\:=\:\dfrac{4+6+5}{120}}$

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$\mapsto\sf{\dfrac{1}{Time}\:=\:\dfrac{15}{120}}$

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$\mapsto\sf{Time\:=\:\dfrac{120}{15}}$

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$\mapsto\sf{Time\:=\:\dfrac{\cancel{120}}{\cancel{15}}}$

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$\mapsto\sf{Time\:=\:8\:days}$

$\sf{\boxed{\boxed{\dag{\red{Time\:taken\:by\:them\: together\:is\:8days}}}}}$