Question

Working together a and b can do a job in 40 days. B and c in 36 days and all three together in 24 days. In how many days can b alone do the job?

Answer 1

Given :  Working together a and b can do a job in 40 days

B and c in 36 days

all three together in 24 days.

To find :  number  of days b alone can do the job

Solution:

Working together a and b can do a job in 40 days  

=> 1/a  + 1/b  = 1/40    Eq1

Working together  b and  c  can do a job in 36 days

=> 1/b + 1/c  = 1/36   Eq2

all three together in 24 days.

=> 1/a + 1/b + 1/c  = 1/24   Eq3

Eq1 + Eq2 - Eq3

=> 1/a + 1/b + 1/b + 1/c - ( 1/a + 1/b + 1/c)  = 1/40 + 1/36 - 1/24

=> 1/b  = (9 + 10  - 15) /360

=> 1/b  = 4/360

=> 1/b = 1/90

=> b = 90

b alone can do the job in 90 days

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Answer 2

Step-by-step explanation:

Given,

• Job done by A & B = 40 days.
• Job done by B & C = 36 days.
• Job done by A, B & C = 24 days.

To Find,

• In how many days can B alone do the job ?

Solution,

Working together A & B can do a job in 40 days.

(Equation 1)

→ 1/a + 1/b

→ 1/40

Working together B & C can do a job in 36 days.

(Equation 2)

→ 1/b + 1/c

→ 1/36

Working all three together can do a job in 24 days.

(Equation 3)

→ 1/a + 1/b + 1/c

→ 1/24

Now putting all the values,

Equation 1 + Equation 2 - Equation 3

→ 1/a + 1/b + 1/b + 1/c - (1/a + 1/b + 1/c)

→ 1/40 + 1/36 - 1/24

→ 1/b = (9 + 10 - 15)/360

→ 1/b = 4/360

→ 1/b = 1/90

→ b = 90

Therefore, B alone can do the job in 90 days.