Question

A and B together can do a job in 2 days; B and C can do it in four days; and A and C in $2\dfrac{2}{5}$ days. The number of days required for A to do the job alone is:
A. 1
B. 3
C. 6
D. 12

Answer 1

Hint: We will be using the concept of time and work to make equations with the help of data given then we will solve these equations to find the required answer.

Complete step-by-step answer:
Now, we will first let the work A, B and C do in 1 day be a, b, c respectively.
Now, we have been given that A and B can do a job in 2 days. So, we have work done by A and B in 1 day \[=\dfrac{1}{2}\]
$a+b=\dfrac{1}{2}............\left( 1 \right)$
Also, B and C can do the same work in 4 days. So, we have,
Work done by B and C in 1 day $=\dfrac{1}{4}$
$b+c=\dfrac{1}{4}............\left( 2 \right)$
Also, we have been given that A and C can complete the work in $2\dfrac{2}{5}$days or $\dfrac{12}{5}$ days. So, we have,
$a+c=\dfrac{5}{12}............\left( 3 \right)$
Now, we will add (1), (2) and (3)
$2\left( a+b+c \right)=\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{5}{12}$
Now, taking 12 as LCM, we have,
$\begin{align}
  & 2\left( a+b+c \right)=\dfrac{6+3+5}{12} \\
 & a+b+c=\dfrac{14}{2\times 12} \\
 & a+b+c=\dfrac{7}{12} \\
\end{align}$
Now, we will substitute the value of b + c from (2).
$\begin{align}
  & a+\dfrac{1}{4}=\dfrac{7}{12} \\
 & a=\dfrac{7}{12}-\dfrac{1}{4} \\
 & a=\dfrac{7-3}{12} \\
 & a=\dfrac{1}{3} \\
\end{align}$
Now, A can do $\dfrac{1}{3}$th of the work in 1 day. So, he can do the complete work in $\dfrac{1}{\dfrac{1}{3}}=3days$.
So, the correct option is (B).

Note: To solve these types of questions it is important to note that if a man can complete a work in x days then the work he will do in 1 day is $\dfrac{1}{x}$.