A can do 50% of the job in 16 days, B can do one-fourth of the same job in 24 days. Working together, in how many days they can do seven-fourth of the job?

42

A = \(\frac{1}{2}\)W = 16 days = 32 days,

B = \(\frac{1}{4}\)W =24 days = 96 days,

⇒ \(\frac{7}{4}\) of total work = \(\frac{7}{4}\) x 96 = 168 units,

⇒ Time required by A + B to complete 168 units = \(\frac{168}{3+1}\) = \(\frac{168}{4}\) = 42 days,   ..(\(\frac{Work}{Efficiency}\) = Time)