To do a certain work, efficiencies of A and B are in the ratio 7:5. Working together, they can complete the work in $17\frac{1}{2}$ days. In how many days, will B alone complete 50% of the same work?

21

Given,

                    A  :  B

Efficiency       7  :  5

⇒ Both of them complete a work in \( {17 }_{2 }^{1 } \) =\(\frac{35}{2}\) days.

⇒ (7 + 5) x \(\frac{35}{2}\) = 210 units.    ..(Efficiency × Days = Total work)

⇒ Therefore, time taken by B to complete 50% of total work is = 50% of 210 = 105 units.

⇒ \(\frac{105}{5}\) = 21 days.