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### Discussion :: Time and Work

1. X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?

2.  A. 13$$\frac { 1 } { 3 }$$days B. 15 days C. 20 days D. 26 days

Answer : Option A

Explanation :

Work done by X in 8 days =$$[\frac { 1 } { 40 } *8]$$=$$\frac { 1 } { 5 }$$

Remaining work =[1-$$\frac { 1 } { 5 }$$]=$$\frac { 4 } { 5 }$$

Now,$$\frac { 4 } { 5 }$$work is done by Y in 16 days.

Whole work will be done by Y in$$[16*\frac { 5} {4 } ]$$=20 days.

X's 1 day's work =$$\frac { 1 } { 40}$$Y's 1 day's work =$$\frac { 1 } { 20}$$

(X + Y)'s 1 day's work =[$$\frac { 1 } { 40}$$+$$\frac { 1 } { 20}$$]=$$\frac { 3 } { 40}$$

Hence, X and Y will together complete the work in$$( \frac { 40 } {3 } )$$=13$$\frac { 1 } { 3 }$$days

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