Question

A and B together can do a piece of work in 20
days; B and C together can do it in 25 days
while C and A together can do it in 30 days.
How long will they take to finish the work,
working all together? How long each take to
do the same work?​

Answer 1

Answer:

A and B together can do 1 by 20th piece of work in one day.

B and C together can do one by 25th piece of work in one day.

C and A together can do 1 by 30th piece of work in one day.

if we add all these

2 times (A and B and C) together can do 1/20 + 1/25 + 1/30 piece of work on 1 day

2 times (A and B and C) together can do 37/300 part of work in 1 day

(A and B and C) together can do 37/600 part of work in 1 day

all together they will need 600/37 days i.e. 16.22 days.

subtracting first two

A - C = 1/20 - 1/25 = 1/100

last one is

A + C = 1/30

adding the two

2A = 13/300

A can do 13/600 part of work on 1 day

A can do same work in 600/13 days 46.15 days

only B can 1/20 - 13/600 = 17/600 part of work in 1 day

B can do same work in 600/17 days i.e. 35.29 days

again C an do 1/30 - 13/600 = 7/600

C alone can do 7/600 part of the work in 1 day

so C can do the work in 600/7 days i.e. 85.72 days

Step-by-step explanation:

given