Find the correct relationship between two quantities. Quantity I- In how many days A can alone do the work if A and B can do a work in 60 days, B and C can do a work in 45 days, C and A can do work in 30 days. Quantity II- A and B together can complete three fourth of a work in 45days. They starts work together but after 20days A left the work and remaining work completed by B in 100 days. In how many days A can alone complete the total work ?

Quantity I: Given (A+B)=60 days, (B+C)=45 days, (C+A)=30 days. Adding: 2(A+B+C) work per day = 1/60+1/45+1/30 = 13/180. So (A+B+C) = 13/360. Then A alone = 13/360 - 1/45 = 13/360-8/360 = 5/360 = 1/72 days. Quantity II: A and B do 3/4 work in 45 days together, so their rate = (3/4)/45 = 1/60 per day. After 20 days, work done = 20/60 = 1/3. Remaining work = 2/3 done by B in 100 days, so B's rate = (2/3)/100 = 1/150. Then A's rate = 1/60 - 1/150 = 5/300-2/300 = 3/300 = 1/100. So A alone = 100 days. Since 100 > 72, Quantity II > Quantity I.