Question

A can do a piece of work in 10 days, and B can do the same work in 20 days. With the help of C, they finished the work in 4 days. C can do the work in how many days, working alone?

Answer 1

Hint: In this question let the number of days in which C can finish the work be a variable. Use a unitary method to find the work done by A per day, and similarly do it for B. Formulate an equation involving the variable as they can finish the work in 4 days, all together.

Complete step-by-step answer:
Let C finish the work in x days.

Given data

A can do a piece of work in 10 days.

B can do a piece of work in 20 days.

And with the help of C they finished the work in 4 days.

So one day work of A = (1/10).

One day work of B = (1/20).

And one day work of C = (1/x).

A, B and C together one day work = (1/4).

So one day work of A + one day work of B + one day work of C = A, B and C together one day work.

$ \Rightarrow \dfrac{1}{{10}} + \dfrac{1}{{20}} + \dfrac{1}{x} = \dfrac{1}{4}$

Now simplify the equation we have,

$ \Rightarrow \dfrac{1}{x} = \dfrac{1}{4} - \dfrac{1}{{10}} - \dfrac{1}{{20}}$

$ \Rightarrow \dfrac{1}{x} = \dfrac{{\left( {10 \times 20} \right) - \left( {4 \times 20} \right) -

\left( {10 \times 4} \right)}}{{\left( {20 \times 10 \times 4} \right)}}$

$ \Rightarrow \dfrac{1}{x} = \dfrac{{200 - 80 - 40}}{{800}} = \dfrac{{80}}{{800}} =

 \dfrac{1}{{10}}$

Therefore x one day work is (1/10)

$ \Rightarrow x = 10$ Days.

Therefore C can finish the work alone in 10 days.

So this is the required answer.

Note: These types of work and time problems are based upon the unitary concepts of taking out an individual's work per day. There is no determined formula while solving such problems, as they are mostly based upon general mathematics.