Directions (55–57): Read the following passage carefully and answer the questions given below. $p$ men can do a work in $q$ days and $q$ women can do the same work in $p$ days. If 20 men and 16 women can do the work together, they can complete the whole work in $53 frac{1}{3}$ days. 20 me

Question

Directions (55–57): Read the following passage carefully and answer the questions given below. $p$ men can do a work in $q$ days and $q$ women can do the same work in $p$ days. If 20 men and 16 women can do the work together, they can complete the whole work in $53	frac{1}{3}$ days. 20 men and 24 women started working together and they did the work for $0.6x$ days, and $y$ boys did the remaining work in $0.45x$ days. If the whole work is completed in $x$ days by $y$ boys, then find the value of $x$.

Accepted Answer

25. Let one man's 1-day work be $m$ and one woman's 1-day work be $w$. From $p$ men in $q$ days and $q$ women in $p$ days doing the same work, we get $pm = qw$ and hence a relation between their efficiencies. Using the fact that 20 men and 16 women finish the work in $53	frac{1}{3}$ days gives the total work and the combined rate. Substituting into the second condition and equating the work completed leads to $x=25$.

Solution

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