A and B together can complete a piece of work in 12 days and B and C together in 15 days

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52.

A, B and C can do a work separately in 16, 32 and 48 days respectively. They started the work together but B left off 8 days and C six days before the completion of the work. In what time is the work finished? 

• 10 days

• 9 days

• 12 days

• 14 days

C.

12 days

Let the work is finished in x days.

Home » Aptitude » Time and Work » Question

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A and B can do a piece of work in 12 days. B and C In 15 days, and C and A in 20 days. How much time will A alone take to finish the Job?

Solution

Time taken by $A$ and $B$ to complete a unit of work $=12$ days

Therefore, work done by $A$ and $B$ in $1$ day $=\frac{1}{12}$ units of work

Similarly,

Work done by $B$ and $C$ is $1$ day $=\frac{1}{15}$ units of work

Work done by $A$ and $C$ in $1$ day $=\frac{1}{20}$ units of work

Therefore, total work done by $A,B$ and $C$ $=\frac{1}{2}\times (\frac{1}{12}+\frac{1}{15}+\frac{1}{20})$

LCM of $12,15$ and $20$ is $60$

$=\frac{1}{2}\times \left(\frac{1\times 5+1\times 4+1\times 3}{60}\right)$

$=\frac{1}{2}\times \left(\frac{12}{60}\right)$

$=\frac{1}{10}$ units of work

Therefore, work done by $A$ alone in $1$ day $=$ Total work done $-$ Work done by $B$ and $C$

$=\frac{1}{10}-\frac{1}{15}$

$=\frac{1\times 3-1\times 2}{30}$

$=\frac{1}{30}$ units of work

Hence, time taken by $A$ to complete a unit of work $=30$ days

Mathematics

Secondary School Mathematics VIII

Standard VIII