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?

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