Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

LohaHridoy
  1. 3 : 4
  2. 4 : 3
  3. 5 : 3
  4. Data inadequate

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Answer: Option 2

$$\eqalign{ & \left( {20 \times 16} \right){\text{women}}\,{\text{can}}\,{\text{complete}}\,{\text{the}}\,{\text{work}}\,{\text{in}}\,{\text{1}}\,{\text{day}} \cr & \therefore {\text{1}}\,{\text{woman's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{320}} \cr & \left( {16 \times 15} \right)\,{\text{men}}\,{\text{can}}\,{\text{complete}}\,{\text{the}}\,{\text{work}}\,{\text{in}}\,{\text{1}}\,{\text{day}} \cr & \therefore {\text{1}}\,{\text{man's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{240}} \cr & {\text{So,}}\,{\text{required}}\,{\text{ratio}} \cr & = \frac{1}{{240}}:\frac{1}{{320}} \cr & = \frac{1}{3}:\frac{1}{4} \cr & = 4:3\,\left( {{\text{cross}}\,{\text{multiplied}}} \right) \cr} $$

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