Instructions

In each of the following questions, a question is followed by information given in three statements. You have to study the question alongwith the statements and decide the information given in which of the statement (s) is necessary to answer the question.

Question 110

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 3 3/7 days.
III. If 10 men work for 3 days and there after 10 women replace them, the remaining work is completed in 4 days.

Solution

I : 10 men complete work in 6 days

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

II : $$(10 \times \frac{24}{7})$$ men + $$(10 \times \frac{24}{7})$$ women = 1 day

=> $$(\frac{240}{7})$$ men's 1 day's work + $$(\frac{240}{7})$$ women's 1 day's work = 1

=> $$(\frac{240}{7} \times \frac{1}{60})$$+ $$(\frac{240}{7})$$ women's 1 day's work = 1

=> $$(\frac{240}{7})$$ women's 1 day's work = $$1 - \frac{4}{7} = \frac{3}{7}$$

=> 10 women's 1 day's work = $$\frac{3}{7} \times \frac{7}{240} \times 10 = \frac{1}{8}$$

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

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

Again, repeating the same procedure, we can find out the time taken by 10 women to finish the work.

Thus, any 2 of the three statements is sufficient.


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