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 a workman as C ,in how many days A alone will do the same work.

Answer 1

A alone can do the same work in 30 days.

Step-by-step explanation:

A and B together can do do a piece of work in 12 days

So, A and B one day work = A + B = 1 / 12

B and C can do it in 15 days

So, B and C one day work = B + C = 1 / 15 --- Eq( 1 )

A is twice as good as workman as C

=> A = 2C

Substituting A = 2C in A + B = 1 / 12

=> 2C + B = 1 / 12 ----- Eq( 2 )

Subtracting Eq( 1 ) from ( 2 )

=> 2C + B - ( B + C ) = 1 / 12 - 1 / 15

=> 2C + B - B - C = ( 5 - 4 ) / 60

=> C = 1 / 60

Substituting C = 1 / 60 in A = 2C

=> A = 2( 1 / 60 ) = 1 / 30

Hence A alone can do it in 30 days.

Answer 2

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 a workman as C ,in how many days A alone will do the same work ?

Solution -

The above question states the following information -

A and B together can do a piece of work in 12 days, B and C together can do it in 15 days.

So, the required time taken by A and B to complete a piece of work is 12 days.

This can be also expressed as -

The required work done by A and B in a day is ( 1 / 12 ) the of the total work done .

So, our first Equation becomes -

$\sf{\purple{ \boxed{\boxed{ \leadsto{ A + B = \dfrac{1}{12} }}}}}$

Similarly, the following can also be stated ..

The required work done by B and C in a day is ( 1 / 15 ) the of the total work done .

So, our second Equation becomes -

$\sf{\orange{ \boxed{\boxed{ \leadsto{ B + C = \dfrac{1}{15} }}}}}$

Now, we gave the following information -

A is twice as good a workman as C .

This can be expressed in terms of a mathematical expression as -

A = 2C

So,

Now, let us substitute this value into the first Equation .

$\sf{\red { \boxed{\boxed{ \therefore{ B + 2C = \dfrac{1}{12} }}}}}$

Now, let us solve the two equations in the terms of C

So, Subtracting there second Equation from the first one

i.e, B + 2C - B - C = C

$\sf{\orange{ \boxed{\boxed{ \leadsto{ B + C = \dfrac{1}{15} }}}}}$

$\sf{\red { \boxed{\boxed{ \leadsto{ B + 2C = \dfrac{1}{12} }}}}}$

$\sf{\blue { \boxed{\boxed{ \mapsto{C = \dfrac{1}{15} - \dfrac{1}{12} = \dfrac{1}{60} }}}}}$

Now, as we stated above ,

A is twice as good a workman as C .

A = 2C

So,

A = 2 × ( 1 / 60 ) = ( 1 / 30 )

So, A can do ( 1/30) the of the work in a day .

Therefore A takes 30 days to complete the required work .

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