Question

a can complete a task alone in 8 days , while b takes 12 days to do it by herself together with c ittakes them 4 days to comlete the work.if c and d can complete the task in 15 days .then how many days will d need to complete the task by herself

Answer 1

Answer:

d will need 40 days to complete task by herself

Step-by-step explanation:

a can complete a task alone in 8 days

a's 1 day work  = 1/8

b takes 12 days to do it by herself

b's 1 day work  = 1/12

Let say c can complete work in c Days

c's 1 day work  = 1/c

a , b & c together  completes work in 4 days

a , b & c together   1 day work = 1/4

=> 1/8 + 1/12 + 1/c  = 1/4

=>  1/c = 1/4  - 1/8  - 1/12

=> 1/c = (1/24)( 6  - 3  - 2)

=> 1/c = 1/24

Let Say d complete task in d days

d's 1 day work = 1/d

c & d complete work in 15 days

c & d 's 1 day work = 1/15

=> 1/c + 1/d  = 1/15

=> 1/24 + 1/d = 1/15

=> 1/d = 1/15 - 1/24

=> 1/d = (1/120) ( 8 - 5)

=> 1/d = 3/120

=> 1/d = 1/40

=> d = 40

d will need 40 days to complete task by herself