Time and Work - Arithmetic Aptitude Questions and Answers

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Discussion :: Time and Work

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?

18 days

24 days

30 days

36 days

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Answer : Option A

Explanation :

2(A + B + C)'s 1 day's work =[ $\frac { 1 } { 30 }$ + $\frac { 1 } { 2 4}$ + $\frac { 1 } { 2 0} ]$ = $\frac { 1 5} {1 20 }$ = $\frac { 1 } { 8 }$

Therefore, (A + B + C)'s 1 day's work = $\frac { 1 } { 2*8 }$ = $\frac { 1 } { 16 }$

Work done by A, B, C in 10 days = $\frac { 10 } { 16 }$ = $\frac { 5 } { 8 }$

Remaining work =[1- $\frac { 5 } { 8 }$ ]= $\frac { 3 } { 8 }$

A's 1 day's work =[ $\frac { 1 } { 16 }$ - $\frac { 1 } { 24 } ]$ = $\frac { 1 } { 48 }$

Now, $\frac { 1 } { 48 }$ work is done by A in 1 day.

So, $\frac { 3 } { 8 }$ work will be done by A in[48 $*\frac { 3 } {8 }$ ]=18days

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