$A$ and $B$ can do a piece of work in $15$ days. If $A$’s one day work is $1\dfrac{1}{2}$ times the one day work of $B$. Find in how many days can each do the work?

Question

$A$ and $B$ can do a piece of work in $15$ days. If $A$’s one day work is $1\dfrac{1}{2}$ times the one  day work of $B$. Find in how many days can each do the work?

Vedantu Content Team · Accepted Answer

Hint: Let us assume that $A$ alone can do the work in $x$ days and similarly $B$ alone can do the same work in $y$ days.Then one day work of $A$$ = \dfrac{1}{x}$ One day work of $B$$ = \dfrac{1}{y}$Now we have to do the rest calculation.Complete step-by-step answer:In this question it is given that $A$ and $B$ can do a piece of work in $15$ days. It is also given that $A$’s one day work is $1\dfrac{1}{2}$ times the one day work of $B$.Now we have to calculate the total time taken by $A$ alone and $B$ alone to do this work.So first of all let us assume that:$A$ alone can do the work in $x$ days. $B$ alone can do the same work in $y$ days.So if $A$ alone can do the work in $x$ days, then one day work of $A$$ = \dfrac{1}{x}$ And if  $B$ alone can do the same work in $y$ days, then one day work of $B$$ = \dfrac{1}{y}$And in this question we know the relation between both one day’s work.$A$’s one day work is $1\dfrac{1}{2}$ times the one day work of $B$.Here we know that One day work of $A$$ = \dfrac{1}{x}$ One day work of $B$$ = \dfrac{1}{y}$And $\dfrac{1}{x} = 1\dfrac{1}{2}.\dfrac{1}{y}$ $\dfrac{1}{x} = \dfrac{3}{{2y}}$ $y = \dfrac{{3x}}{2}$    $ -  -  -  -  - \left( 1 \right)$Now it is also given that they can complete work together in $15$ days. So one day work of together is:$\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{1}{{15}}$   $ -  -  -  -  - \left( 2 \right)$Now putting the value of $y = \dfrac{{3x}}{2}$ in equation $\left( 2 \right)$$\dfrac{1}{x} + \dfrac{2}{{3x}} = \dfrac{1}{{15}}$ $\dfrac{{3 + 2}}{{3x}} = \dfrac{1}{{15}}$$\dfrac{5}{{3x}} = \dfrac{1}{{15}}$$x = 25$daysSimilarly $y = \dfrac{{3x}}{2}$$ = \dfrac{{75}}{2}$ daysSo $A$ alone can do the work in $25$ days.$B$ alone can do it in $\dfrac{{75}}{2}$ days.Note: In this type of question you need to find the two questions. First equation you will get from the statement that they can complete work together in $15$ days. And the second equation, you will get from the statement that $A$’s one day work is $1\dfrac{1}{2}$ times the one day work of $B$.

$A$ and $B$ can do a piece of work in $15$ days. If $A$’s one day work is $1\dfrac{1}{2}$ times the one day work of $B$. Find in how many days can each do the work?

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$A$ and $B$ can do a piece of work in $15$ days. If $A$’s one day work is $1\dfrac{1}{2}$ times the one day work of $B$. Find in how many days can each do the work?

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