Question

# A particular work can be completed by $$6$$ men and $$6$$ women in $$24$$ days, whereas the same work can be completed by $$8$$ men and $$12$$ women in $$15$$ days. Find the time taken by $$4$$ men and $$6$$ women to complete the same work .

A
20 days
B
30 days
C
50 days
D
40 days

Solution

## The correct option is B $$30$$ daysFrom the question, we have($$6$$ men and $$6$$ women) $$1$$ day work $$=\dfrac{1}{24}$$($$12$$ men and $$12$$ women)$$1$$ day work$$=\dfrac{1}{12}$$   ...     (1)($$8$$ men and $$12$$ women)$$1$$ day work$$=\dfrac{1}{15}$$     ...    (2)Subtracting (1) and (2), we get$$4$$ men work $$=\dfrac{1}{12}$$  $$-\dfrac{1}{15}$$ $$=\dfrac{1}{60}$$  $$2$$ men work $$=\dfrac{1}{120}$$  $$4$$ men and $$6$$ women work $$=1$$ day work of $$6$$ men and $$6$$ women  $$-1$$ day work of $$2$$ men.$$=\dfrac{1}{24}$$ $$-\dfrac{1}{120}$$ $$=\dfrac{4}{120}$$  $$=\dfrac{1}{30}$$  The time taken by $$4$$ men and $$6$$ women to complete the same work $$= 30$$ days.Hence, option B.Mathematics

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