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 $=1:2$.

12 men can complete a piece of work in 36 days. 18 women can complete the same piece of work in 60 days. 8 men and 20 women work together for 20 days. If only women were to complete the remaining piece of work in 4 days, how many women would be required ?

Answer:

Explanation:

$12\times 36$ men can complete the work in $1$ day.

$18\times 6$ women can complete the work in $1$ day.

$12\times 36$ men $=18\times 60$ women $\Rightarrow$ 2 men = 5 women.

Now 8 men + 20 women = (4 $\times$ 5) + 20 women $=20+20$ = 40 women 18 women complete the work in 60 days.

40 women's 20 days work $= \frac{(40\times 20)}{(18\times 60)}$ $= \frac{20}{27}$

Remaining work $=\frac{7}{27}$

$18\times 60$ women do 1 work in 1 day

so that 1 woman does $=\frac{1}{(18\times 60)}$ work in 1 day

In 4 days, 1 woman does $=\frac{4}{(18\times 60)}$ $=\frac{1}{(18\times 15)}$ work

$\frac{7}{27}$ Work is done by  $\frac{(18\times 15\times 7 )}{27}$ = 70 women.

5 men and 2 boys working together can do four times as much work as a man and a boy. Working capacities of a woman and a boy are in the ratio :

Answer:

Explanation:

Let $1$ man $1$ day work $=x$

$1$ boy $1$ day work $=y$

Then, $5x+2y$ $=4(x+y)$

$\Rightarrow x=2y$

$\Rightarrow \frac{x}{y}=\frac{2}{1}$

$\Rightarrow x:y=2:1$

A, B and C can do a piece of work in 6, 8 and 10 days respectively. They begin to work together. A continues to work till it is finished, B leaves off 1 day before and C leaves off $\frac{1}{2}$ day before the work is finished. In what time is the work finished ?

Answer:

Explanation:

Let the work be finished in $x$ days.

Then, $A$ works for $x$ days.

$B$ works for $(x-1)$ days.

$C$ works for $(x-\frac{1}{2})$ days.

Also $A,B,C$ can do $\frac{1}{6},\frac{1}{8},\frac{1}{10}th$ of work daily, respectively.

From the problem,

$\left[\frac{1}{6}x+\frac{1}{8}(x-1)+\frac{1}{10}\left(x-\frac{1}{2}\right)\right]$ $=1$

(i.e) $\left(\frac{1}{6}+\frac{1}{8}+\frac{1}{10}\right)x-\left(\frac{1}{8}+\frac{1}{20}\right)$ $=1$

$\left(\frac{20+15+12}{120}\right)x-\left(\frac{5+2}{40}\right)$ $=1$

$\frac{47x}{120}$ $=\left(1+\frac{7}{40}\right)$ $=\frac{47}{40}$ $\Rightarrow x=3$

$\therefore$ The work was finished in 3 days.

Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?

Answer:

Explanation:

Number of pages typed by Ravi in $1$ hour $=\frac{32}{6}$ $=\frac{16}{3}$.

Number of pages typed by Kumar in $1$ hour $=\frac{40}{5}$ $=8$.

Number of pages typed by both in $1$ hour $=\left(\frac{16}{3}+8\right)$ $=\frac{40}{3}$.

$\therefore$ Time taken by both to type $110$ pages $=\left(110\times\frac{3}{40}\right)$ hours.

$=8\frac{1}{4}$ hour or $8$ hours $15$ minutes.

A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work ?

Answer:

Explanation:

$B$'s 10 days' work $=\frac{1}{15}\times 10$ $=\frac{2}{3}$

Remaining work $=\left(1-\frac{2}{3}\right)$ $=\frac{1}{3}$

Now, $\frac{1}{18}$ work is done by $A$ in $1$ day.

$\frac{1}{3}$ work is done by $A$ in $18\times\frac{1}{3}$ = 6 days.

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