1. 8 men can finish a piece of work in 21 days. 14 men started working and after 3 days were replaced by 9 women. These 9 women finished the remaining work in 24 days. In how many days 9 women can finish the whole work ?
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By: anil on 05 May 2019 01.40 am
Let efficiency of 1 man = $$x$$ units/day Efficiency of 1 woman = $$y$$ units/day Since, 8 men finish the work in 21 days Let total work = $$x imes 8 imes 21 = 168x$$ units Initially, 14 men worked for 3 days => worked completed = $$x imes 14 imes 3 = 42x$$ units Work left = $$168x - 42x = 126x$$ units ---------------------(i) Now, 9 women complete this work in 24 days => work done by women = $$y imes 9 imes 24 = 216y$$ units --------(iI) From eqn (i) & (ii), we get : $$126x = 216y$$ => $$frac{x}{y} = frac{216}{126} = frac{12}{7}$$ $$ herefore$$ Number of days taken by 9 women to finish the work = $$frac{168x}{9y} = frac{168}{9} imes frac{12}{7}$$ = $$24 imes frac{4}{3} = 32$$ days
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