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If $20$ men working $7$ hours a day can do a piece of work in $10$ days, in how many days will $15$ men working for $8$ hours a day do the same piece of work?

  1. $\dfrac{320}{21} \text{ days} \\$
  2. $\dfrac{35}{3} \text{ days} \\$
  3. $\dfrac{105}{16} \text{ days} \\$
  4. $\dfrac{21}{5}\text{ days} \\$
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Answer is B

$\frac{15}{20}=\frac{10}{x}$  [ men and hours are inversely proportional]

$\frac{7}{8}=\frac{x}{10}$   [ days and hours are inversely proportional]

x  = $\frac{10*20*7}{15*8} = \frac{35}{3}$ days

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