A can complete the whole work in 10 days while B can do it in 20 days and C can do it in 30 days. They start working together but after 2 days; A left the work and after 1 day more of A, B also left the work then in how many days the whole work will be completed ?

Option 1 : 19.5 days

Given:

A can do in 10 days

B can do in 20 days

C can do in 30 days

Calculation:

Total work = LCM(10, 20, 30) = 60 unit

One day work of A = 6

One day work of B = 3

One day work of C = 2

For the first 2 days, A, B and C works together

∴ The work completed = (6 + 3 + 2) × 2 = 22 unit

For the next 1 day B and C works together (∵ A left)

∴ The work completed = (3 + 2) × 1 = 5 unit

Remaining work = 60- (22 + 5) = 33 unit

C alone works for the remaining days since B also left

Number of days C requires to complete the work = 33/2 = 16.5 days

∴ The whole work will be completed in 16.5 + 2 + 1 = 19.5 days