Question

7. A. B and C working together can finish a piece of work in 8 hours. A alone can do it
20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same
work?




plss help me guys​

Answer 1

A. B and C working together can finish a piece of work in 8 hours. A alone can do it

20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same

work?

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.

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Answer 2

$\huge\mathtt\pink{✁Answer}$

Given :-

A ,B ,C working together can finish a work in 8 hours

A Can alone do the work in 20 hours

B can alone do the work in 24 hours

To Find :-

In how many hours will C can alone do the same work ?

Solution :-

★A ,B ,C working together can finish a work in 8 hours

∴ In one hour they can do 1/8th of work

★A Can alone do the work in 20 hours

∴ In 1 hour A can alone finish 1/20th of work

★B can alone do the work in 24 hours

$∴ \frac{1}{x} = \frac{1}{30}$

In 1 hour B can alone finish 1/24th of work

Let, 1 hour C can do 1/x th of work

So,

$\frac{1}{20} + \frac{1}{24} + \frac{1}{x} = \frac{1}{8}$

$\frac{1}{x} = \frac{1}{8} - ( \frac{1}{20} + \frac{1}{24} )$

$\frac{1}{x} = \frac{1}{8} - \frac{44}{20 \times 24}$

$\frac{1}{x} = \frac{1}{8} - \frac{11}{120}$

$\frac{1}{x} = \frac{15 - 11}{120}$

$\frac{1}{x} = \frac{4}{120}$

$∴ \frac{1}{x} = \frac{1}{30}$

Hence, C can do the same work in 30 hours