# Time and work questions

Time and Work aptitude questions and answers are an important part of any competitive exam. It helps test the applicant's knowledge of the relationship between time, work, and rate. Several types of questions are asked in the aptitude test related to time and work which require a methodical approach to solve them. Here are some examples of the most common types of aptitude questions and answers related to Time and Work.

1. While working 7 hours a day, A alone can complete a piece of work in 6 days and B alone in 8 days. In what time would they complete it together, working 8 hours a day ?

A alone can complete the work in 42 days working 1 hour daily. Similarly, B will take 56 days working 1 hour daily.

A 's 1 day's work $=\frac{1}{42}$

$\mathrm{B}$ 's 1 day's work $=\frac{1}{56}$

$(A+B)$ 's 1 day's work

$=\frac{1}{42}+\frac{1}{56}=\frac{4+3}{168}=\frac{7}{168}$

$\therefore$ Time taken by $(A+B)$ working

8 hours daily $=\frac{168}{7 \times 8}=3$ days

1. A and B can separately complete a piece of work in 20 days and 30 days respectively. They worked together for some time, then B left the work. If A completed the rest of the work in 10 days, then B worked for ?

Here, $m =20, n =30, p = x$

and time taken by A alone = 10

$\Rightarrow 10=\frac{m n-p(m+n)}{n}$

$10=\frac{30 \times 20-x(30+20)}{30}$

$300=600-x 50$

$50 x=300 x=6$

$\Rightarrow B$ worked for 6 days

1. A certain factory employed 600 men and 400 women and the average wage was 2.55 per day. If a women got 50 paise less than a man, the daily wages of a man and a woman were ?

Let daily wages of a man be Rs. $x$

$\therefore$ Daily wages of a woman

$= Rs. \left(x-\frac{1}{2}\right)$

According to the question,

$600 x+400\left(x-\frac{1}{2}\right)$

$=1000 \times 2.55$

$\Rightarrow 600 x+400 x-200=2550$

$\Rightarrow 1000 x=2550+200=2750$

$\Rightarrow x=\frac{2750}{1000}= Rs .2 .75$

$\therefore$ Daily wages of a woman $=$ Rs. $(2.75-0.5)$

$=$ Rs. 2.25

1. A certain number of persons can complete a piece of work in 55 days. If there were 6 persons more, the work could be finished in 11 days less. How many persons were originally there ?

Originally, let there be $x$ men Now, more men, less days $(x+6): x:: 55: 44$

So, $\frac{x+6}{x}=\frac{55}{44}=\frac{5}{4}$

or $\quad 5 x=4 x+24$

or $x=24$

1. A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?

A's 1-hour work= $\frac{1}{4}$
B and C together 1 hour's work =$\frac{1}{3}$
A and C together 1 hour's work=$\frac{1}{2}$
A,B,C together 1 hour's work=$\frac{1}{4}$+$\frac{1}{3}$=$\frac{7}{12}$
B's 1 hour's work =$\frac{7}{12}$-$\frac{1}{2}$=$\frac{1}{12}$