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Question

2 women and 5 men can together finish an embroidery work in 4 days ,, while 3 women and 6 men can finish it in 3 days. Finish the time taken by 1 woman alone to finish the work , and also that taken by 1 man alone.


Solution

Number of days required 
For women be x
For men be y
Work done by women in 1 day= $$\dfrac{1}{x}$$
Work done by men in 1 day = $$\dfrac{1}{y}$$
$$4 \left ( \dfrac{2}{x} +  \dfrac{5}{y}\right ) = 1$$
$$3\left ( \dfrac{3}{x} + \dfrac{6}{y}\right ) = 1 $$
Let $$\dfrac{1}{x}  = p and \dfrac{1}{y} = q$$.
$$\therefore 8p+20q=1,9p+18q=1$$
From both the equation
$$9\frac{(1-20q)}{8}+18q=1$$
$$q=\frac{1}{36}$$
$$p=\frac{1}{18}$$
$$\therefore$$ 1 women will finish work in 18 days

Mathematics

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