Question

A and B can do a piece of work in \[8\] days B and C can do the same work in \[12\] days. If A, B and C can complete the same work in \[6\] days in how many days can A and C complete the same work?

A. \[8\]
B. \[10\]
C. \[12\]
D. \[16\]

Answer 1

Hint- If we have to solve problems of this kind at first always seek to figure out what work is completed in a single day. Here we assume the days taken by A and C to complete the work as a variable by using the statement we can find out the variable's value further.

Complete step-by-step answer:
Given statements A and B can do a piece of work in \[8\] days B and C can do the same work in \[12\]days. A, B and C can complete the same work in \[6\]days.
Let A and C complete the work in \[x\] days
The one day work of A and C is \[ = {\text{ }}1/x\]
Now, we will calculate the work done by A and B in a single day
A and B can do a given piece of work in \[8\] days.
One day work of A and B is \[ = {\text{ }}1/8\]
Similarly, we will calculate the work done by B and C in a single day
B and C can do the same work in \[12\] days
The one day work of B and C is \[ = {\text{ }}1/12\]
It is given that A, B and C can do a given piece of work in \[6\] days.
So, The one day work of A, B and C is \[1/6\]
Thus, (A+B+B+C+C+A)’s one day’s work \[ = 1/8 + 1/12 + 1/x\]
\[
  (\;3x + 2x + 24)/24x \\
  2 \times 1/6 = (5x + 24)/24x \\
  8x = 5x + 24 \\
  3x = 24 \\
  x = 8 \\
 \]

Hence, A and C together complete the work in \[8\] day.
A is the correct option.

Note- If a person is working for one day/hour\[ = {\text{ }}1/n\], then he completes the job in \['n'\] days/hours. When the ratio of men needed to complete a job is \[m:{\text{ }}n\] then the ratio of time they take will be \[n:m\].