Question

A takes 6 days less than B to do work. If both A and B working together can do it in 4 days, how many days will B take to finish it?

Answer 1

Hint- In this question, let variable be number of days B takes to finish the work and calculate number of days A alone take to finish it. Calculate A’s one Day’s work and B’s one day’s work and equate it to one day’s work of both A & B together.

Complete step-by-step answer:

Let number of B takes alone to finish the work $ = x{\text{ days}}$

Number of days A takes alone to finish the work $ = (x - 6){\text{ days}}$

A’s one day’s work = $\dfrac{1}{{x - 6}}$

B’s one day’s work = $\dfrac{1}{x}$

A’s and B’s together one day’s work = $\dfrac{1}{4}$

According to question,
$
  \dfrac{1}{{x - 6}} + \dfrac{1}{x} = \dfrac{1}{4} \\
  \dfrac{{x + \left( {x - 6} \right)}}{{x\left( {x - 6} \right)}} = \dfrac{1}{4} \\
  2x - 6 = \dfrac{{x\left( {x - 6} \right)}}{4} \\
  8x - 24 = {x^2} - 6x \\
  {x^2} - 14x + 24 = 0 \\
  \left( {x - 12} \right)\left( {x - 2} \right) = 0 \\
  x = 2{\text{ }}or{\text{ }}12 \\
$
$x = 2$ not possible as A’s number of days to finish work will be meaningless.
$ \Rightarrow x = 12$

Hence, B takes 12 days to finish the work alone.

Note- These types of problems related to time and work can be solved easily by the method of taking lcm. But it is quite hard to understand directly. For solving such problems we must start with finding persons each day’s work and then moving on finding them for given no of days.