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### Discussion :: Time and Work

1. 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?

2.  A. 18 days B. 24 days C. 30 days D. 36 days

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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