A is 4 times as fast as B and is,therefore,ab | vedclass

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(A) Let the time taken by $B$ to complete the work be $x$ days.Since $A$ is $4$ times as fast as $B$,the time taken by $A$ to complete the same work i

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(A) Let the time taken by $B$ to complete the work be $x$ days.Since $A$ is $4$ times as fast as $B$,the time taken by $A$ to complete the same work is $\frac{x}{4}$ days.According to the problem,$A$ takes $45$ days less than $B$,so $x - \frac{x}{4} = 45$.Solving for $x$: $\frac{3x}{4} = 45$,which gives $x = 60$ days.Thus,$B$ takes $60$ days and $A$ takes $\frac{60}{4} = 15$ days.The work done by $A$ in $1$ day is $\frac{1}{15}$ and by $B$ in $1$ day is $\frac{1}{60}$.Working together,their $1$ day's work is $\frac{1}{15} + \frac{1}{60} = \frac{4+1}{60} = \frac{5}{60} = \frac{1}{12}$.Therefore,$A$ and $B$ together can complete the work in $12$ days.

$A$ is $4$ times as fast as $B$ and is,therefore,able to complete a work in $45$ $days$ less than $B$. $A$ and $B$,working together,can complete the work in (in $days$)

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