A alone can do a piece of work in 10 days. A and B together can do the same piece of work in $\frac{20}{3}$ days. A, B and C together can do the same piece of work in $\frac{40}{7}$ days. In how many days can B and C together do the same piece of work?

$\frac{40}{3}$

A = 10 days,

A + B = \(\frac{20}{3}\) days,

A + B + C = \(\frac{40}{7}\) days,

⇒ A + B = 6 (Efficiency)

⇒ 4 + B = 6,

⇒ B = 2,

Similarily,

⇒ A + B + C = 7

⇒ 6 + C = 7

⇒ C = 1,

Therefore, time required for B + C to complete the work = \(\frac{40}{3}\) days,        ..(\(\frac{Work}{Efficiency}\) = Time)