Mohan can do a bit of work in 25 days which can be completed by Sohan in 20 days. Both together labour for 5 days and afterward Mohan leaves off. How long will Sohan take to complete the remaining work? Let, total work = 100 (LCM of 25 and 20) Mohan, (25) > Total Work < 4 Sohan, (20) 100 5 5 days work of Mohan and Sohan = (4 + 5) × 5 = 45 Remaining work = 100 – 45 = 55 Time taken by Sohan to complete remaining work = $$\frac{55}{5}$$ = 11 days 2. In a lock-and-key making factory, one machine produces only locks at a rate of 100 locks per minute. After producing every 1000 locks, the machine needs to be cleaned, which takes 5 minutes. The second machine produces only keys at a rate of 75 keys per minute. After making every 1500 keys, this machine needs to be cleaned, which takes 10 minutes. If both machines start working together to make locks and keys, what is the minimum time in minutes it will take to produce a set of 9000 lock-and-key pairs?