Question

A and B together can complete a task in 20 days. B and C can complete the same task in 30 days. A and C together can complete the same task in 40 days. What is the ratio of number of days taken by A when completing the same task alone to the number of days taken by C when completing the same task alone?

Answer 1

Answer:

A : C :: 1 : 5

Step-by-step explanation:

A , B , C are the days taken by A, B , C respectively to complete task.

A and B together can complete a task in 20 days

=> 1/A + 1/B  = 1/20

B and C can complete the same task in 30 days

=> 1/B + 1/C   = 1/30

A and C together can complete the same task in 40 days.

=> 1/A + 1/C = 1/40

Adding all three

1/A + 1/B + 1/B + 1/C + 1/A + 1/C  = 1/20 + 1/30 + 1/40

=> 2( 1/A + 1/B + 1/C) = (6 + 4 + 3)/120

=>  1/A + 1/B + 1/C = 13/240

1/A + 1/B + 1/C  -  (1/B + 1/C) = 13/240 -  1/30

=> 1/A  = 5/240

=> A = 48

1/A + 1/B + 1/C  -  ( 1/A + 1/B) = 13/240 -  1/20

=> 1/C  = 1/240

=> C = 240

A : C :: 48 : 240

=> A : C :: 1 : 5