time and work

Question

A takes 3 times long as B+C together and B takes 4 times as long as A+C together. All 3 working together takes 24 days to complete, then time taken by A alone to complete???

 

 

Answer 1

Hi Shivam

let A = the number of work units of the 24 that are completed by person A

let B = the number of work units of the 24 that are completed by person B

let C = the number of work units of the 24 that are completed by person C

then

A + B + C =24

3A = (B+C)

now substitute

A + 3A = 24

4A = 24

A equals 6 (so out of the 24 units of work person A worked 6 of those)

4B = A + C

4B = 6 + C

go back to the original equation

A + B + C = 24

B + A + C = 24

B + 4B = 24

5B = 24

B = 4.8 (so out of the 24 units of work person B worked 4.8 of those)

now find C

6 + 4.8 + C = 24

C = 24 -10.8

C = 13.2 (so out of the 24 units of work person C worked 13.2 of those)

person A completed 6/24 or 1/4 of the job

person B completed 4.8/24 or 1/5 of the job

person C completed 13.2/24 or 11/20 of the job

1/4 + 1/5 + 11/20

5/20 + 4/20 + 11/20 = 20/20 equals 100% of the work

 

So now find how long it would take A to do the job alone

 

in 24 days A did 6/24 or 1/4 of the job

 

So it would take him 4 times that to complete the whole job or 24 * 4 = 96 days