Question

A and B together can complete a task in 7 days. B alone can do it in 20 days. What part of the work was carried out by A?
I.A completed the job after A and B worked together for 5 days.
II.Part of the work done by A could have been done by B and C together in 6 days.

A.I alone is sufficient while II alone is not sufficient to answer.
B.II alone is sufficient while I alone is not sufficient to answer.
C.Either I or II alone sufficient to answer
D.Both I and II are not sufficient to answer.
E.Both I and II are necessary to answer.

Answer 1

Hint: In this question, we need to determine the part (or piece) of the work done by A alone to complete the work such that A and B work together only for 5 days. For this, we will use the unitary method and the concept which states that the total work completed in a day is the summation of the work done by the individual workers in a day.

Complete step-by-step answer:
Let A and B complete the work while working alone be A and B, respectively.
According to the question,
A and B complete a work in 7 days working together. So, the amount of work completed by A and B in a day is given as:
$\dfrac{1}{A} + \dfrac{1}{B} = \dfrac{1}{7} - - - - (i)$

From part I of the question, A and B worked together for 5 days so, the work completed in 5 days by A and B is given as
\[
  {\left( {\dfrac{1}{A} + \dfrac{1}{B}} \right)_{one{\text{ day}}}} = \dfrac{1}{7} \\
  {\left( {\dfrac{1}{A} + \dfrac{1}{B}} \right)_{{\text{5 days}}}} = \dfrac{5}{7} \\
 \]

As, the total work is denoted by 1 so, the remaining work that has to be done by A alone is given as$1 - \dfrac{5}{7} = \dfrac{{7 - 5}}{7} = \dfrac{2}{7}$
Hence, $\dfrac{2}{7}$ of the total work is done by A alone after B left the job after 5 days.
So, part I is sufficient to answer the question.
From part II of the question, it has been mentioned that work done by A could have been done by B and C together in 6 days, but we don’t have any other relation with the variable C and so we cannot determine the work completed by C and consequently by A.
Hence, part II is not at all sufficient to answer the question.
So, I alone is sufficient while II alone is not sufficient to answer.
Option A is correct.
So, the correct answer is “Option A”.

Note: In these types of questions, we need to check both the parts alone and in combination also to get the correct result. Moreover, many times none of the given parts in the question are sufficient to answer the question.