A and B can do a job alone in 12 text{ days} | vedclass

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Question

(A) Work done by $A$ in $1 	ext{ day} = \frac{1}{12}$.Work done by $B$ in $1 	ext{ day} = \frac{1}{15}$.Work done by $A$ in $6 	ext{ days} = 6 	im

Vedclass · Accepted Answer

$3 \frac{1}{3}$

Vedclass · Answer

(A) Work done by $A$ in $1 	ext{ day} = \frac{1}{12}$.Work done by $B$ in $1 	ext{ day} = \frac{1}{15}$.Work done by $A$ in $6 	ext{ days} = 6 	imes \frac{1}{12} = \frac{1}{2}$.Remaining work = $1 - \frac{1}{2} = \frac{1}{2}$.Combined work rate of $A$ and $B$ = $\frac{1}{12} + \frac{1}{15} = \frac{5+4}{60} = \frac{9}{60} = \frac{3}{20}$.Time taken by $A$ and $B$ together to complete the remaining $\frac{1}{2}$ work = $\frac{1/2}{3/20} = \frac{1}{2} 	imes \frac{20}{3} = \frac{10}{3} = 3 \frac{1}{3} 	ext{ days}$.Since $B$ joined after $6 	ext{ days}$ and worked until the end,$B$ worked for $3 \frac{1}{3} 	ext{ days}$.

$A$ and $B$ can do a job alone in $12 \text{ days}$ and $15 \text{ days}$ respectively. $A$ starts the work and after $6 \text{ days}$,$B$ also joins to finish the work together. For how many days did $B$ actually work on the job?

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