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 $=1:2$.

A can do a piece of work in 12 days, while B alone can do it in 15 days, with the help of C they can finish it in 5 days. If they are paid Rs. 960 for the whole work, what is the share of A?

Answer:

Explanation:

A's share for 5 days $=\frac{1}{12}\times 5\times 960$ = 400 Rs. 

A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day ?

Answer:

Explanation:

A's $2$ day's work $=\left(\frac{1}{20}\times 2\right)$ $=\frac{1}{10}$.

$(A+B+C)'s$ $1$ day work $=\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{60}\right)$ =$\frac{1}{10}$.

Work done in $3$ days $=\left(\frac{1}{10}+\frac{1}{10}\right)$ $=\frac{1}{5}$.

Now, $\frac{1}{5}$ work is done in $3$ days.

$\therefore$ Whole work will be done in $(3\times 5)$ = 15 days.

95 men had provisions for 200 days. After 5 days, 30 men died due to an epidemic. The remaining food will last for how many days ?

Answer:

Explanation:

The remaining food is sufficient for $95$ men for $195$ days.

But, now remaining men $=(95-30)=65$.

Less men, More days (Indirect)

$\therefore65:95::195:x$

$\Leftrightarrow 65x=95\times 195$

$\Leftrightarrow x=\frac{(95\times 195)}{65}$ = 285 days

Twelve children take sixteen days to complete a work which can be completed by eight adults in twelve days. Sixteen adults started working and after three days ten adults left and four children joined them. How many days will they take to complete the remaining work ?

Answer:

Explanation:

$12$ children take $16$ days to complete the work.

$\Rightarrow$ $1$ child takes $16\times 12=192$ days to complete the work.

$\Rightarrow$ Work done by $1$ child in $1$ day $=\frac{1}{192}$

$8$ adults take $12$ days to complete the work.

$\Rightarrow$ $1$ adult takes $12\times 8=96$ days to complete the work.

$\Rightarrow$ Work done by $1$ adult in $1$ day $=\frac{1}{96}$.

$16$ adults worked for $3$ days

Work completed $=16\times\frac{1}{96}\times 3$ $=\frac{1}{2}$.

Remaining work $=1-\frac{1}{2}$ $=\frac{1}{2}$

The remaining work is done by $6$ adults and $4$ children

Work done in $1$ day $=6\times\frac{1}{96}+4\times\frac{1}{192}$ $=\frac{1}{16}+\frac{1}{48}$ $=\frac{1}{12}$.

Required days to complete the remaining work $=\frac{1}{2}\div\frac{1}{12}$ = 6 days.

A certain number of men completed a piece of work in 60 days. If there were 8 men more, the work could be finished in 10 days less. How many men were originally there ?

Answer:

Explanation:

Suppose total number of men $=x$

$x$ men can work a job in $60$ days 

$x$ men can work $\frac{1}{60}$ job in $1$ day 

$1$ man can work $\frac{1}{60x}$ in 1 day ------(1) 

$x+8$ can do the same job in $50$ days

Similarly, $1$ man can do $\frac{1}{50(x+8)}$ job in $1$ day ------(2) 

from (1) and (2), $\frac{1}{60x}$ $=\frac{1}{50(x+8)}$ 

Solving the equation, $x$ = 40 men.

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