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### Discussion :: Time and Work

1.  In how many days can 10 women finish a work?

I .10 men can complete the work in 6 days.

II.10 men and 10 women together can complete the work in $$\left(\frac{33}{7}\right)$$ days.

III.If 10 men work for 3 days and thereafter 10 women replace them, the remaining work in completed in 4 days.

2.  A. Any two of the three B. I and II only C. II and III only D. I and III only E. None of these

Answer : Option A

Explanation :

I. (10 x 6) men can complete the work in 1 day.

1 man's 1 day's work =$$\frac { 1 } { 60 }$$

II.$$[10*\frac { 24} {7 } ]$$men +$$[10*\frac { 24} {7 } ]$$women can complete the work in 1 day

$$( \frac {2 40 } { 7} )$$men's 1 day work +$$( \frac {2 40 } { 7} )$$women's 1 day work = 1

$$[ \frac {2 40 } { 7}$$$$*\frac {1} {60 } ]$$+$$( \frac {2 40 } { 7} )$$women's 1 day's work = 1

$$( \frac {2 40 } { 7} )$$women's 1 day's work =[1-$$\frac { 4 } { 7 }$$]=$$\frac {3 } { 7 }$$

10 women's 1 day's work =[$$\frac {3 } { 7 } *$$$$\frac {7 } { 240 } *10]$$=$$\frac { 1 } { 8 }$$

So, 10 women can finish the work in 8 days.

III. (10 men's work for 3 days) + (10 women's work for 4 days) = 1

(10 x 3) men's 1 day's work + (10 x 4) women's 1 day's work = 1

30 men's 1 day's work + 40 women's 1 day's work = 1

Thus, I and III will give us the answer.

And, II and III will give us the answer.

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