Discussion Forum



Each of the questions given below consists of two statements numbered I and II given below it. Please read the questions carefully and decide whether the data provided in the statement(s) is / are sufficient to answer the given question.

1)

$X$ alone can complete a work in $12$ days. How many days will $X,Y,Z$ together take to complete the work ?.

I. $X$ and $Y$ together can complete the work in $3$ days.

II. $Y$ and $Z$ together can complete the work in $6$ days.


A) I alone sufficient while II alone not sufficient to answer

B) II alone sufficient while I alone 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:

Option E

Explanation:

Given: $Y$'s $1$ days work $=\frac{1}{12}$.

I. gives, $(X+Y)$'s $1$ day's work $=\frac{1}{3}$.

$\Rightarrow$ $X$'s $1$ day's work $=\left(\frac{1}{3}-\frac{1}{12}\right)$ $=\frac{3}{12}$ $=\frac{1}{4}$.

II. gives, $(Y+Z)$'s $1$ day's work $=\frac{1}{6}$

$\Rightarrow$ $Z$'s $1$ day's work $=\left(\frac{1}{6}-\frac{1}{12}\right)$ $=\frac{1}{12}$.

$\therefore$ $(X+Y+Z)$'s $1$ day work $=\left(\frac{1}{4}+\frac{1}{12}+\frac{1}{12}\right)$ $=\frac{5}{12}$.

Hence, they will all finish the work in $\frac{12}{5}$ $=2\frac{2}{5}$ days.

Thus, I and II both are necessary to get the answer.

$\therefore$ Correct answer is (E).