Question

# A, B and C complete a work working alone in 10, 15 and 20 days respectively If all of them work together to complete the work what fraction of the work would have been done by B?${\text{A}}{\text{. }}\dfrac{4}{{13}} \\ {\text{B}}{\text{. }}\dfrac{1}{2} \\ {\text{C}}{\text{. }}\dfrac{1}{3} \\ {\text{D}}{\text{. }}\dfrac{6}{{13}} \\$

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Hint: Let us first go through the unitary method for solving the question. First we have to find one day of work for each worker. Then find total work done by all together in one day. To find the fraction of single workers.

Here in the question it is given that A finishes the work alone in 10 days.
Therefore the work done by A in a single day is $\dfrac{1}{{10}}$ by applying a unitary method.

It is given that B finishes the work alone in 15 days.
Therefore the work done by B in a single day is $\dfrac{1}{{15}}$ by applying a unitary method.

And it is also given that C finishes the work alone in 20 days.
Therefore the work done by C in a single day is $\dfrac{1}{{20}}$ by applying a unitary method.

Now, let us calculate the total work done by all together in a single day by adding up all their works alone in a single days i.e. (A+B+C)’s one day's work$= \dfrac{1}{{10}} + \dfrac{1}{{15}} + \dfrac{1}{{20}} = \dfrac{{13}}{{60}}$

Now, let’s calculate a fraction of the work that would have been done by B. That means we simply divide the work of B in single days by the work of all together in single days.
I.e. Fraction of work done by B$= \dfrac{{\dfrac{1}{{15}}}}{{\dfrac{{13}}{{60}}}} = \dfrac{1}{{15}} \times \dfrac{{60}}{{13}} = \dfrac{4}{{13}}$.

Hence, the required answer is$\dfrac{4}{{13}}$.

Note: Whenever we face such a type of question the key concept for solving the question is first we have to find the work of a single worker in a single day by applying a unitary method. By doing this we are able to add their works in a single day so we are able to find the amount of work done by all together in a single day. Then for finding the fraction simply divide the work done by that worker by the total work done by all together.