X can complete half of the work in 20 days and Y can do one-fifth of the same work in 10 days. X started the work and left after 8 days. Then Y took over to complete the remaining work. The total number of days taken by them to complete the work is:

48 days

X = \(\frac{1}{2}\)W = 20 days = 40 days,

Y = \(\frac{1}{5}\)W = 10 days = 50 days,

⇒ X worked for 8 days and left = 5 x 8 = 40 units,   ..(Efficiency × Days = Total work)

⇒ Remaining work = 200 - 40 = 160 units,

⇒ Y completed the remaining work = \(\frac{160}{4}\) = 40 days,   ..(\(\frac{Work}{Efficiency}\) = Time)

⇒ Therefore, total time taken to complete the total work = 8 + 40 = 48 days,