1.

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?​

Answer»

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.


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