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 6 men and 8 boys can do a piece of work in 10 days and 26 men and 48 boys can do the same work in 2 days, the time taken by 15 men and 20 boys to do the same type of work will be

Answer:

Explanation:

Given (6 Men +8 boys)$\times$10 = (26 men + 48 boys)$\times$2

60 men + 80 boys = 52 men  + 96 boys

1 man = 2 boys

15 men + 20 boys = 30 boys +20 boys = 50 boys

6 men + 8 boys = 12 boys + 8 boys = 20 boys

$\therefore$ 20 boys = 10 days

50 boys = $x$

$x=\frac{(20\times 10)}{50}$ = 4 days

12 children takes 16 days to complete a work which can be completed by 8 adult in 12 days. 16 adults started working and after 3 days,10 adults left and 4 children joined them. How many days will they take to complete the remaining work?

Answer:

Explanation:

1 child 1 day work $=\frac{1}{192}$

1 adult 1 day work $=\frac{1}{96}$

Work done by 16 adults in 3 days $=\frac{1}{96}\times 16\times 3$ $=\frac{1}{2}$

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

(6 adult + 4 children ) 1 day work $=\left(\frac{6}{96}+\frac{4}{192}\right)$ $=\frac{1}{12}$

$\frac{1}{12}$ work is done by them in 1 day

 $\frac{1}{2}$ work is done by them $\left(12\times \frac{1}{2}\right)$ = 6 days

Twenty women can do a work in sixteen days .16 men can complete the same work in 15 days. What is the ratio between the capacity of a man and a woman?

Answer:

Explanation:

$(20\times 16)$ women can complete the work in 1 day.

1 woman 1 day work $=\frac{1}{320}$.

$(16\times 15)$ men can complete the work in 1 day.

1 man 1 day work $=\frac{1}{240}$.

Required ratio $=\frac{1}{240}:\frac{1}{320}$ = 4 : 3

A contractor undertakes to dig a canal 12 km long in 350 days and employes 45 men .He finds after 200 days of working that only $4\frac{1}{2}$ km of canal have been completed. How many extra men must be employed to finish the work in time?

Answer:

Explanation:

$4.5$ km in $200$ days by $45$ men

now remaining $7.5$ km in $150$ days by $45+x$ men

$\left(\frac{200\times 45}{4.5}\right)$ $=\left(\frac{(45+x)\times 150}{7.5}\right)$

on solving this we get $x=55$.

So 55 men extra are required.

A,B,C are employed to do a piece of work for Rs.529. A and B together are supposed to do $\frac{19}{23}$ of the work and B and C together $\frac{8}{23}$ of the work. What is the share of A?

Answer:

Explanation:

$(A+B)$’s work $=\frac{19}{23}$

$C$’swork $=\left(1-\frac{19}{23}\right)$ $=\frac{4}{23}$

$A$’s work $=\frac{19}{23}-\frac{4}{23}$ $=\frac{15}{23}$

Ratio of work done by $A,B,C$ $=15:4:4$

$A$’s share $=\frac{15}{23}\times 529$ = 345

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