Question

A and B together can do a piece of work in 12 days ; B and C together can do it in 15 days . if A is twice as good as workman as C , in how many days A alone will do the same work ?​

Answer 1

Ok Let’s start by this.

=ℎ×
W
o
r
k
d
o
n
e
=
r
a
t
e
o
f
t
h
e
p
e
r
s
o
n
×
t
i
m
e
t
a
k
e
n


=×=
W
=
r
×
t
=
r
t


Now if A and B are working together, the work done is given by

=(+)
W
=
(
r
A
+
r
B
)
t
A
B


where
r
A
is the rate of A and
r
B
is the rate of B and
t
A
B
is time taken for A and B working together to finish the work.

=12
t
A
B
=
12
days

Now For B and C

=(+)
W
=
(
r
B
+
r
C
)
t
B
C


=15
t
B
C
=
15
days

where
r
C
is the rate of C and
t
B
C
is the time taken by both B and C working together to finish the work.

We also know that

=2===>=/2
r
A
=
2
r
C
===>
r
C
=
r
A
/
2
Substitute into ======>=(+)
======>
W
=
(
r
B
+
r
C
)
t
B
C


to get

=(+2)
W
=
(
r
B
+
r
A
2
)
t
B
C


The time taken to finish the work by A alone is given by

=
t
A
=
W
r
A


Equating

=(+)
W
=
(
r
A
+
r
B
)
t
A
B
and =(+2)
W
=
(
r
B
+
r
A
2
)
t
B
C


you get

(+)==(+2)
(
r
A
+
r
B
)
t
A
B
=
W
=
(
r
B
+
r
A
2
)
t
B
C


Solve for
r
B
to get

=1.5
r
B
=
1.5
r
A


Now use

=(+)=2.5
W
=
(
r
A
+
r
B
)
t
A
B
=
2.5
r
A
t
A
B


Substitute the above into

==2.5×=2.5×12=30
t
A
=
W
r
A
=
2.5
×
t
A
B
=
2.5
×
12
=
30
days

Hope this helps u
Mark as brainlist
Good night