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Common Information

Working together, A and B can do a job in 6 days. B and C can do the same job in 10 days, while C and A can do it in 7.5 days.

Q.

Common Information Question: 2/2

How many days will it take for A alone to complete the job?

 A.

8

 B.

6

 C.

10

 D.

20

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Solution:
Option(C) is correct

Now if we try to eliminate choices in this question, we know that $A$ and $B$ together take 6 days to complete the job.

Therefore, $A$ alone will take more than 6 days to complete the job. Therefore, we can eliminate answer choice (2).

In any question, as a rule spend about 5 seconds to see if the answer choices provide any clue to solve the question or help in eliminating one or more obviously absurd choices.

This will help you (1) in reducing the time it will take to do the problem and (2) in increasing your probability of success should you choose to take a guess without actually solving the problem

Let $A$ be the number of days that $A$ will take to complete the job alone, $B$ days for $B$ to complete the job alone and $C$ days for $C$ to complete the job alone.

$A$ and $B$ can do a job in 6 days. They complete \(\left(\dfrac{1}{6}\right)^{th}\) of the job in a day

\(\dfrac{1}{A}+\dfrac{1}{B}=\dfrac{1}{6}........(1)\)

Similarly, $B$ and $C$ will complete \(\left(\dfrac{1}{10}\right)^{th}\) of the job in a day.

\(\dfrac{1}{B}+\dfrac{1}{C}=\dfrac{1}{10}........(2)\)

And $C$ and $A$ will complete \(\left(\dfrac{2}{15}\right)^{th}\)of the job in a day

\(\dfrac{1}{A}+\dfrac{1}{C}=\dfrac{2}{15}........(3)\)

Subtracting eqn (2) from eqn (1)

\(\dfrac{1}{A}-\dfrac{1}{C}=\dfrac{1}{6}-\dfrac{1}{10}=\dfrac{1}{15}........(3)\)

Adding eqn (4) and eqn (3) we get,

\(\dfrac{1}{A}-\dfrac{1}{C}+\dfrac{1}{A}+\dfrac{1}{C}=\dfrac{1}{5}\)

\(\dfrac{1}{A}=\dfrac{1}{10}\)

Thus $A$ does \(\dfrac{1}{10}\) of the job in a day and therefore, will take 10 days to complete the job working alone.

Edit: For an alternative solution, check comment by Bilal Shakil.


(1) Comment(s)


Bilal Shakil
 ()

Since $A$, $B$ and $C$ can complete the job in $\dfrac{1}{5}$ (as calculated in the previous question)

Subtract $ABC - BC = A$

$\dfrac{1}{5}-\dfrac{1}{10} = \dfrac{1}{10}$

Therefore, $A$ alone can complete the job in 10 days.