Arithmetic aptitude :: Time and Work :: Data Sufficiency 1

• 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 $=1:2$.

$X$ 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.

Answer:

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).

Ram and Raj together can complete a task in $7$ days. Raj alone can do it in $20$ days. What part of the work was carried out by Ram?

I. Ram completed the job alone after Ram and Raj worked together for $5$ days.

II. Part of the work done by Ram could have been done by Raj and Ravi together in $6$ days.

Answer:

Explanation:

Raj's $1$ day work $=\frac{1}{20}$

(Ram + Raj)'s $1$ day's work $=\frac{1}{7}$

I.(Ram + Raj)'s $5$ day's work $=\frac{5}{7}$

Remaining work $=\left(1-\frac{5}{7}\right)$ $=\frac{2}{7}$.

$\therefore$ $\frac{2}{7}$ work was carried by Ram.

II. is irrelevent.

$\therefore$ Correct answer is (A).

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