A does half as much work as B in frac{3}{4} o | vedclass

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(A) Let the time taken by $B$ to complete the work be $x$ days.Since $A$ does half as much work as $B$ in $\frac{3}{4}$ of the time,the efficiency of

Vedclass · Accepted Answer

$30$

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(A) Let the time taken by $B$ to complete the work be $x$ days.Since $A$ does half as much work as $B$ in $\frac{3}{4}$ of the time,the efficiency of $A$ relative to $B$ can be calculated.If $B$ does $1$ unit of work in $x$ days,$A$ does $0.5$ units of work in $\frac{3}{4}x$ days.To compare their rates,we find the time $A$ would take to do the same amount of work as $B$ ($1$ unit).Time taken by $A = \frac{3}{4}x 	imes 2 = \frac{3x}{2}$ days.Given that $(A + B)$ together take $18$ days,their combined $1$-day work is $\frac{1}{18}$.So,$\frac{1}{x} + \frac{1}{3x/2} = \frac{1}{18}$.$\frac{1}{x} + \frac{2}{3x} = \frac{1}{18}$.Taking the common denominator: $\frac{3 + 2}{3x} = \frac{1}{18}$.$\frac{5}{3x} = \frac{1}{18}$.$3x = 90$,which gives $x = 30$ days.

$A$ does half as much work as $B$ in $\frac{3}{4}$ of the time. If together they take $18$ days to complete a work,then how much time shall $B$ take to complete it? (in days)

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