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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
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B
30 days
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C
50 days
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D
40 days
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Solution

The correct option is B $$30$$ days
From 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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