X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
📊 Work and Time Calculation 📊
X’s work rate = 1/20 (work done per day)
Y’s work rate = 1/12 (work done per day)
X worked alone for 4 days, completing:
4 days × (1/20) = 1/5 of the work
Remaining work = 1 – 1/5 = 4/5 of the work
Combined work rate of X and Y = (1/20) + (1/12)
= (3 + 5) / 60
= 8/60
= 2/15 (work done per day)
Time taken by X and Y to complete the remaining work = Remaining work / Combined work rate
= (4/5) / (2/15)
= 4/5 × 15/2
= 6 days
Total time taken to complete the work = X’s initial work + X and Y’s combined work
= 4 days + 6 days
= 10 days
🎉 The work lasted for 10 days. 📊
