A can do a piece of work in 12 days. He worked for 6 days and left, and then B finished it in 10 days. If both work together, then in how many days will they finish the same work?

7.5

A = 12 days,

Lets' take A's efficiency as 1.

Therefore, total work = 1 x 12 = 12 units,   ..(Efficiency × Days = Total work)

⇒ A worked for 6 days = 1 x 6 = 6 units,

⇒ Remaining work = 12 - 6 = 6 units,

⇒ B completed the remaining work in 10 days = \(\frac{6}{B}\) = 10 days,

⇒ B = \(\frac{3}{5}\),  (Efficiency)

⇒ Time required by A + B to complete work = \(\frac{12}{1+3/5}\) = \(\frac{12}{8/5}\) = (\frac{15}{2}\) = 7.5 days,   ..(\(\frac{Work}{Efficiency}\) = Time)