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2 Men and 5 women can do a work in 12 days. 5 men and 2 women can do that work in 9 days. Only 3 women can finish the same work in:(a) 36 days(b) 21 days(c) 42 days(d) 30 days |
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Answer» Step-by-step explanation:2 men and 5 women can do a work in 12 days5 men and 2 women can do the work in 9 daysDays taken by 3 women to complete the work➝ Let work done by one man in one DAY = x➝ Let work done by one woman in one day = y➝ By first case given, 2 Men and 5 women can do a work in 12 days 2x + 5y = 1/12 --------(1)➝ By the second case, 5 men and 2 women can finish the work in 9 days. 5x + 2y = 1/9--------(2)➝ Multiply first equation by 5 and second equation by 2 10x + 25y = 5/12-------(3) 10x + 4y = 2/9-------(4)➝ Solving equation 3 and 4 by elimination method, 21y = 5/12 - 2/9 21y = (45 - 24)/108 21 y = 21/108 y = 1/108 y = 1/108➝ Hence one women can complete the work in 108 days.➝ Work completed by 3 women is given by, Days taken by 3 women = ( 1/108 × 3) Days taken by 3 women = 36 days ➝ Hence option a is correct. |
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