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:
Answer & explanation
Correct answer: option 4
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,