Question

Mary and john can do a piece of work in 24 days; john and vino in 30 days; vino and mary in 40 days. if mary, john and vino work together they will complete the work in

Answer 1

Mary M and John J can finish a piece of work = 24 days

(M+J)'s 1 day job = 1/24

John J and Vino V can finish the same amount of work = 30 days

(J+V)'s 1 day job = 1/30

Vino V and Mary M can finish the same piece of work = 40 days

(V+M)'s 1 day job = 1/40

Now

(M+J+V)'s 1 day job = 1/24 + 1/30 + 1/40

2(M+J+V) = (5+4+3)/120

2(M+J+V) = 12/120

2(M+J+V) = 1/10

(M+J+V) = 1/20

They altogether can finish the work in 20 days.

Answer 2

Answer: Mary, John and Vino together will complete the work in 20 days.

Step-by-step explanation:

Given that:

• Mary and John finish the work in 24 days.
• John and Vino finish the work in 30 days.
• Vino and Mary finish the work in 40 days.

We have to find the days to complete the work by all working together.

Finding the one day's work:

1. Mary + John one day's work = 1/24.
2. John + Vino one day's work = 1/30.
3. Vino + Mary one day's work = 1/40.

Now one day's work of Mary, John and Vino together:

$(M+J)+(J+V)+(V+M)=\frac{1}{24}+\frac{1}{30}+\frac{1}{40}$

Solving;

$2(M+J+V)=\frac{5+4+3}{120}$

$2(M+J+V)=\frac{12}{120}$

$2(M+J+V)=\frac{1}{10}$

So, $(M+J+V)=\frac{1}{20}$

Therefore, (Mary + John + Vino)'s one day work is 1/20.

It means they do 1/20th part of the work in one day. Therefore to complete the whole work they need 20 days.

Hence, Mary, John and Vino will together complete the work in 20 days.