A and B together can finish a job in 20 days. B and C together can finish the same job in 30 days. If A and C together can finish it in 24 days, in how many days can A alone finish the job?

examrobotsa's picture
Q: 53 (CAPF/2021)
A and B together can finish a job in 20 days. B and C together can finish the same job in 30 days. If A and C together can finish it in 24 days, in how many days can A alone finish the job?

question_subject: 

Maths

question_exam: 

CAPF

stats: 

0,2,0,0,0,2,0

To find the number of days A alone can finish the job, let`s consider the work done by each pair of workers per day.

Let`s assume that A, B, and C can do 1/x, 1/y, and 1/z of the job per day, respectively.

According to the first statement, A and B together can finish the job in 20 days. This means that the work done by A and B per day is 1/20.

Similarly, B and C together can finish the job in 30 days, so the work done by B and C per day is 1/30.

And according to the third statement, A and C together can finish the job in 24 days, which means the work done by A and C per day is 1/24.

Let`s write equations using these values:

1/x + 1/y = 1/20 ...(1)

1/y + 1/z = 1/30 ...(2)

1/x + 1/z = 1/24 ...(3)

To find the value of x, we need to eliminate y and z from these equations. To do this, let`s subtract equation (2) from equation (3):

(1/x +