Arithmetic aptitude :: Time and Work :: General Questions

• 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 $=1:2$.

If 4 men or 7 boys can do a work in 29 days, then what time will 12 men and 8 boys take to do the same work?

Answer:

Explanation:

4 men = 7 boys

1 man= 7/4 boys

12 men $=\frac{7}{4}\times12$ = 21 boys

(12 men + 8 boys) $=21+8$ = 29 boys

7 boys can do work in 29 days.

$\therefore$ 29 boys can do work in $\left(\frac{29\times 7}{29}\right)$ = 7 days

A garrison of 3000 men has provision for 30 days. If after 10 days they are reinforced by 1000 men ,how long will the provision last?

Answer:

Explanation:

Given that garrison had provision for 3000 men for 30 days

Hence, after 10 days, the remaining food is sufficient for 3000 persons for 20 days

Remaining persons after 10 days $=3000+ 1000$ $= 4000$

Assume that after 10 days,the remaining food is sufficient for $4000$ persons for $x$ days

More men, Less days (Indirect Proportion)

$\Rightarrow Men\quad 3000:4000\}::x:20$

$\Rightarrow 3000\times 20$ $=4000x$

$\Rightarrow x=\frac{3000\times 20}{4000}$ = 15 days.

Mary has m minutes of home work in each of her s subjects. In one hour she completes what part of her home work?

Answer:

Explanation:

Total time taken for all home work in all subjects $= ms$ minutes $=\frac{ms}{60}$ hours

In 1 hr she completes $\frac{60}{ms}$ home work

Two friends take a piece of work for Rs.960. A alone do it in 12 days. B in 16 days. With the assistance of an expert, they finish it in 4 days. How much remuneration the expert should get ?

Answer:

Explanation:

$A$’s 1 day work $=\frac{1}{12}$ $\Rightarrow $ $A$’s 4 days work $\frac{4}{12}$ $=\frac{1}{3}$

$B$’s 1 day work $=\frac{1}{16}$ $\Rightarrow$ $B$’s 4 days work $=\frac{4}{16}$ $=\frac{1}{4}$

Experts 4 days work  $=1-\left(\frac{1}{3}+\frac{1}{4}\right)$ $=\frac{5}{12}$

Ratio of their work  $=\frac{1}{3}:\frac{1}{4}:\frac{5}{12}$  $=4:3:5$

Expert’s share $=\frac{5}{12}\times 960$  =  Rs.400

To complete a work, A take 50% more time than B. If together they take 18 days to complete the work, How much time shall B take to do it?

Answer:

Explanation:

Let $B$ take $x$ days to complete the work .

Then $A$ takes $x+\frac{x}{2}$ $=\frac{3x}{2}$ days to complete the work

Given $\frac{1}{x}+\frac{2}{3x}$ $=\frac{1}{18}$

$\Leftrightarrow x=\frac{18\times 5}{3}$ = 30 days.

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