Question

A and B together can do work in 20 days, B and and C and do the same work in 60 days. Who is the most efficient among A,B and C?

Answer 1

Answer:

IN ONE DAY they do:

A + B= 1/30 of the job or A=1/30-B

A + C= 1/20 of the job or A=1/20-C

C + B= 1/24 of the job or C=1/24-B

1/30-B =1/20-1/24 + B

B = (1/30 - 1/20 + 1/24 ) / 2

So B = 1/ 80

Then we find C = 1/24–1/80 = (20 - 6) /480 = 14/480

C = 7/240

then we find A=1/30-B = 1/30 -1/ 80

A = 5 /240

Now with their rendiment in ten days they do together:

= 10 × ( 5/240 + 1/80 + 7/ 240)

= 15/24

What is left to do is by A only is:

1- 15/24 = 3/8 of the job

Since A does 5/ 240 per day we calculate:

X = (3/8) / (5/240)

X= 18

Whic means that after the first days that they work together the job will be finished by A alone in another 18 days.