Question

A, B and C working together can finish a piece of work in 4 hours. A alone can do it in
12 hours and B alone can do it in 10 hours. In how many hours will C alone do thesame work?​

Answer 1

Answer:

Answer

A,B,C working together complete a work in 8 hours.

∴ In one hour they can complete

8

1

th of work.

A can alone do the work in 20hr

∴ In one hour A can complete

20

1

th of work.

B can alone do the work in 24hr.

∴ In one hour B can do

24

1

th of work.

Let in one hour C can do

x

1

th of work.

∴

20

1

+

24

!

+

x

1

=

8

1

⇒

x

1

=

8

1

−(

20

1

+

24

1

)

=

8

1

−

20×24

44

=

8

1

−

120

11

=

120

15−11

=

120

4

=

30

1

∴ C can do the same work in 30 hours.

Answer 2

Answer:

15 days

Step-by-step explanation:

let the work done by A in 1/x hrs and by B in 1/y hrs and by c in 1/z hrs

Therefore a part of work done in an hour will be

$( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} ) = \frac{1}{4}$

Now we know that the work done by A alone is in 10 hrs and B can done a work in 12 hrs

Therefore,

$( \frac{1}{10} + \frac{1}{12} + \frac{1}{z} ) = \frac{1}{4}$

$4( \frac{1}{10} + \frac{1}{12} + \frac{1}{z} ) = 1$

$4( \frac{12}{120} + \frac{10}{120} + \frac{1}{z} ) = 1$

$4( \frac{22}{120} + \frac{1}{z} ) = 1$

$\frac{22}{30} + \frac{4}{z} = 1$

$\frac{4}{z} = \frac{30}{30} - \frac{22}{30}$

$\frac{4}{z} = \frac{8}{30}$

Therefore

z=15 hrs

hence C can do same work in 15hrs alone