To complete a project, 18 women take 4 more days than the number of days taken by 12 men. If eight men complete the project in 9 days, how much work will be left when 15 women and 12 men together work for 3 days?

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1. Let the time taken by 12 men be $x$ days. Then 18 women take $x+4$ days.

2. Total work = 1. Rate of 12 men = $\dfrac{1}{x}$, so one man’s rate = $\dfrac{1}{12x}$. Rate of 18 women = $\dfrac{1}{x+4}$, so one woman’s rate = $\dfrac{1}{18(x+4)}$.

3. Given 8 men finish in 9 days, so one man’s rate = $\dfrac{1}{8	imes9}=\dfrac{1}{72}$. Equate: $\dfrac{1}{12x}=\dfrac{1}{72}\Rightarrow x=6$.

4. Thus 18 women take $6+4=10$ days, so one woman’s rate = $\dfrac{1}{18	imes10}=\dfrac{1}{180}$.

5. Combined rate of 15 women and 12 men: $15\cdot\dfrac{1}{180}+12\cdot\dfrac{1}{72}=\dfrac{1}{12}+\dfrac{1}{6}=\dfrac{1}{4}$ (work per day).

6. Work done in 3 days = $3	imes\dfrac{1}{4}=\dfrac{3}{4}$. Remaining work = $1-\dfrac{3}{4}=\dfrac{1}{4}$.

FINAL_ANSWER: d

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