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Question

A and B can do a piece of work in 30 days , while B and C can do the same work in 24 days and C and A in 20 days .They all work together for 10 days when B and C leave . How many days more will A take to finish the work ?


A

18 days

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B

24 days

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C

30 days

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D

36 days

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Solution

The correct option is A

18 days


Time taken by A and B to do the work =30 days

So work done by A and B in one day =130

Time taken by B and C to do the work =24 days

So work done by B and C in one day =124

Time taken by C and A to do the work =20 days

So work done by C and A in one day =120

So work done by A,B,C in one day =130+124+120

A+B=130,B+C=124,C+A=120

A+B+B+C+C+A=130+124+1202A+2B+2C=130+124+1202(A+B+C)=1×4+1×5+1×61202(A+B+C)=4+5+61202(A+B+C)=15120=18(A+B+C)=12×8=116

Therefore one day work of A+B+C =116

So work done in 10 days of A+B+C=10×116=58

So remaining work done by A is =1-58=38

Now A one day work is

=(A+B+C)-(B+C)(onedaywork)=116-124=1×3-1×248=3-248=148

Time taken by A to do the work =48 days

But A done only 38 work alone =38×48=3×6=18days

Hence A will take 18 more days to complete the work .

Therefore option(A) is the correct answer and all other options are incorrect answers .


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