Question

A,b and c togather do a work in 12 days if a and c togather do double of b and a and b do triple of c then in how many days they do the work alone

Answer 1

Answer:

a = 28.8 Days

b = 36 Days

c = 48  Days

Step-by-step explanation:

Let say a complete work alone = a days

then a's 1 day work = 1/a

Let say b complete work alone = b days

then b's 1 day work = 1/b

Let say c complete work alone = c days

then c's 1 day work = 1/c

A B & C together 1 days work = 1/a + 1/b + 1/c

They complete work in 12 days so 1 day work = 1/12

=> 1/a + 1/b + 1/c = 1/12   - Eq 1

a and c together do double of b

1/a + 1/c = 2(1/b)    - Eq2

a and b do triple of c

1/a + 1/b = 3(1/c)   - Eq2

Putting value of 1/a + 1/c from eq2 into Eq 1

2/b + 1/b = 1/12

=> 3/b = 1/12

=> b = 36 Days

Now Putting value of 1/a + 1/b from eq3 into Eq 1

3/c + 1/c = 1/12

=> 4/c = 1/12

=> c = 48  Days

putting values of b & c in Eq 1

1/a + 1/36 + 1/48 = 1/12

=> 144/a + 4 + 3 = 12   (multiplying by 144 both sides)

=> 144/a = 5

=> a = 144/5

=> a = 28.8 Days