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 a workman as C, then in how many days will B alone can do it?
Answers
Step-by-step explanation:
Let one days word of A = 1/a
One days word of B = 1/b
One days word of C = 1/c
A and B can do a piece of work in 12 days.
\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{1}{12}
a
1
+
b
1
=
12
1
.... (1)
B and C together can do it in 15 days.
\dfrac{1}{b}+\dfrac{1}{c}=\dfrac{1}{15}
b
1
+
c
1
=
15
1
.... (2)
A is twice as good a workman as C.
\dfrac{1}{a}=2\times \dfrac{1}{c}
a
1
=2×
c
1
From (1) and (2) substitute the values of 1/a and 1/c.
\dfrac{1}{12}-\dfrac{1}{b}=2(\dfrac{1}{15}-\dfrac{1}{b})
12
1
−
b
1
=2(
15
1
−
b
1
)
\dfrac{1}{12}-\dfrac{1}{b}=\dfrac{2}{15}-\dfrac{2}{b}
12
1
−
b
1
=
15
2
−
b
2
\dfrac{2}{b}-\dfrac{1}{b}=\dfrac{2}{15}-\dfrac{1}{12}
b
2
−
b
1
=
15
2
−
12
1
\dfrac{1}{b}=\dfrac{8-5}{60}
b
1
=
60
8−5
\dfrac{1}{b}=\dfrac{1}{20}
b
1
=
20
1
b=20b=20
Therefore, B alone can do it in 20 days.