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AnilSinghBora
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Formulate the following problems as a pair of equations, and hence find their solutions: (ii) 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. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone. Q.2(2)

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In exercise 3.6 of class 10th of Pair of linear equations in two variables. How i solve this problem because it is very important Formulate the following problems as a pair of equations, and hence find their solutions: (ii) 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. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.

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  1. Let us consider,

    Number of days taken by women to finish the work = x

    Number of days taken by men to finish the work = y

    Work done by women in one day = 1/x

    Work done by women in one day = 1/y

    As per the question given,

    4(2/x + 5/y) = 1

    (2/x + 5/y) = 1/4

    And, 3(3/x + 6/y) = 1

    (3/x + 6/y) = 1/3

    Now, put 1/x=m and 1/y=n, we get,

    2m + 5n = 1/4 => 8m + 20n = 1…………………(1)

    3m + 6n =1/3 => 9m + 18n = 1………………….(2)

    Now, by cross multiplication method, we get here,

    m/(20-18) = n/(9-8) = 1/ (180-144)

    m/2 = n/1 = 1/36

    m/2 = 1/36

    m = 1/18

    m = 1/x = 1/18

    or x = 18

    n = 1/y = 1/36

    y = 36

    Therefore,

    Number of days taken by women to finish the work = 18

    Number of days taken by men to finish the work = 36.

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