Question

A and B can do a work in 15 days BandC can do the same work in 20 days and AandCcan do it in 12 days can each of them can do the work indivisualy​

Answer 1

Step-by-step explanation:

Let A finish work in a days, B in b days, C in c days. Amount of work done by A in one day is 1/a.

A and B can do work in 15 days. Therefore the work done by both in one day is 1/15

i.e. 1/a + 1/b = 1/15

Similarly, 1/b + 1/c = 1/20

1/c + 1/a = 1/12

adding them and dividing by 2 on both side, we get, 1/a + 1/b + 1/c = 0.5 * ( 1/15 +1/20 + 1/12) = 1/10

Now subtracting the first 3 equations from this equation one by one, we get, 1/c = 1/30

1/b = 1/60, 1/a = 1/20.

Therefore a= 20, b=60, c=30

Answer 2

Solution :-

A and B can do a work in 15 days

So, A and B's one day work = A + B = 1/15

==> A + B = 1/15 -- Eq(1)

B and C cans do a work in 20 days

So, B and C's one day work = B + C = 1/20

==> B + C = 1/20 --- Eq(2)

A and C can do a work in 12 days

A and C's one day work = A + C = 1/12

==> A + C = 1/12 --- Eq(3)

Adding Eq(1) , (2), (3)

==> A + B + B + C + A + C = 1/15 + 1/20 + 1/12

==> 2A + 2B + 2C = (4 + 3 + 5) / 60

==> 2(A + B + C) = 12 / 60

==> 2(A + B + C) = 1/5

==> A + B + C = 1/(5 * 2) = 1/10

Finding A's 1 day work

==> A + B + C = 1/10

==> A = 1/10 - ( B + C) = 1/10 - 1/20 = (2 - 1)/20 = 1/20

A's one day work = 1/20

So, A can complete the work in 20 days

Finding B's one day work

==> A + B + C = 1/10

==> B = 1/20 - (A + C) = 1/10 - 1/12 = (6 - 5)/60 = 1/60

B's one day work = 1/60

So, B can do it in 60 days

Finding C's one day work

==> A + B + C = 1/10

==> C = 1/10 - ( A + B ) = 1/10 - 1/15 = (3 - 2)/30 = 1/30

C's one day work = 1/30

So, C can do it in 30 days.