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### Discussion :: Time and Work

1. X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

2.  A. 6 days B. 10 days C. 15 days D. 20 days

Explanation :

Work done by X in 4 days =[$$\frac { 1 } { 20 } *4]$$=$$\frac { 1 } {5}$$

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

(X + Y)'s 1 day's work =[$$\frac { 1 } { 20 }$$+$$\frac { 1 } { 12 }$$]=$$\frac { 8} {60}$$=$$\frac { 2 } {15}$$

Now,$$\frac { 2 } {15}$$work is done by X and Y in 1 day

So,$$\frac { 4 } {5}$$work will be done by X and Y in[$$\frac { 15 } {2} *$$$$\frac { 4 } {5}$$]=6days

Hence, total time taken = (6 + 4) days = 10 days.

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