A and B can do a work in 45 text{ days} and 4 | vedclass

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(B) Let $A$ leave after $x$ days.$A$'s one day work = $\frac{1}{45}$$B$'s one day work = $\frac{1}{40}$Since $A$ and $B$ worked together for $x$ days,

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(B) Let $A$ leave after $x$ days.$A$'s one day work = $\frac{1}{45}$$B$'s one day work = $\frac{1}{40}$Since $A$ and $B$ worked together for $x$ days,and $B$ worked alone for $23$ days,the total work done is:$x \left( \frac{1}{45} + \frac{1}{40} \right) + 23 \left( \frac{1}{40} \right) = 1$$\frac{x}{45} + \frac{x}{40} + \frac{23}{40} = 1$$\frac{x}{45} + \frac{x+23}{40} = 1$Taking the $LCM$ of $45$ and $40$,which is $360$:$\frac{8x + 9(x+23)}{360} = 1$$8x + 9x + 207 = 360$$17x = 360 - 207$$17x = 153$$x = 9$Therefore,$A$ left after $9$ days.

$A$ and $B$ can do a work in $45 \text{ days}$ and $40 \text{ days}$,respectively. They began the work together,but $A$ left after some time and $B$ completed the remaining work in $23 \text{ days}$. After how many days of the start of the work did $A$ leave?

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