Discussion Forum



Please study each questions below and all the three statements, numbered I, II and III, and decide whether any information provided in the statement(s) is redundant and can be dispensed with while answering the given question.

1)

In how many days can the work be completed by $X$, $Y$ and $Z$ together ?

I. $X$ and $Y$ together can complete the work in $6$ days.

II. $Y$ and $Z$ together can complete the work in $3\frac{3}{4}$ days.

III. $X$ and $Z$ together can complete the work in $3\frac{1}{3}$ days.


A) Any one of the three

B) I only

C) II only

D) III only

E) I and II and III necessary to answer

Answer:

Option E

Explanation:

I. $(X+Y)$'s $1$ day's work $=\frac{1}{6}$.

II. $(Y+Z)$'s $1$ day's work $=\frac{4}{15}$.

III. $(X+Z)$'s $1$ day's work $=\frac{3}{10}$.

Adding, we get $2(X+Y+Z)$'s $1$ day's work $=\left(\frac{1}{6}+\frac{4}{15}+\frac{3}{10}\right)$ $=\frac{22}{30}$.

$\Rightarrow$ $(X+Y+Z)$'s $1$ day's work $=\left(\frac{1}{2}\times\frac{22}{30}\right)$ $=\frac{11}{30}$.

Thus, $X$, $Y$ and $Z$ together can finish the work in $\frac{30}{11}$ days.

Hence I, II and III are necessary to answer the question.

$\therefore$ Correct answer is (E).