Arithmetic aptitude :: Time and Work :: Data Sufficiency 3

• Time and Work - General Questions
• Time and Work - Data Sufficiency 1
• Time and Work - Data Sufficiency 2
• Time and Work - Data Sufficiency 3
• Time and Work - Important Formulas and Facts

If $A$ can do a part of work in $n$ days, then $A$'s $1$ day work $=\frac{1}{n}$.

If $A$'s $1$ day's work $=\frac{1}{n}$, then $A$ can complete the work in $n$ days.

If $A$ is twice as good a worker as $B$, then:

Ratio of the work done by $A$ and $B$ $=2:1$.

Ratio of times taken by $A$ and $B$ to finish a work $=1:2$.

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.

Answer:

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).

$8$ boys and $14$ girls are working together. After working for $3$ days, $5$ boys and $8$ girls leave the work. How many more days will be required to complete the work?

I. $19$ boys and $12$ girls together can complete the work in $18$ days.

II. $16$ boys can complete $\frac{2}{3}$ of the work in $16$ days.

III. In $1$ day, the work done by $3$ boys is equal to the work done by $4$ girls.

Answer:

Explanation:

Clearly, I only gives the answer.

Similarly, II only gives the answer.

And, III only gives the answer.

Correct answer is (D).

• Time and Work - General Questions
• Time and Work - Data Sufficiency 1
• Time and Work - Data Sufficiency 2
• Time and Work - Data Sufficiency 3