Time and Work

Time and Work

How many people can complete the task within how many days or how long it will take to complete the given work or how
much work one person can do etc.


Basic Formulas

• If a person can do a piece of work in x days, then person's one day work is (1/x)
• If a person's 1 day's work is (1 / x) then the person will complete the work in x days.
• While solving the problems assume the work done by person to be equal to 1. 

 Example sum
1. A alone can do a piece of work in 6 days, B alone can do the same work in 12 days. In how many days can A and B together completes the same work? 

A's 1 day work = (1 / 6)
B's 1 day's work= (1 / 12)
(A + B)'s l day's work 
= (1/6)+(1 / 12)
=(1/4)(A + B )
 will completethe work in 4 days

2. Ravi gets Rs. 110 for every day that he works. If he earns Rs. 2750 in a month of 31 days, for how many days did he work?Required number of days = ( 2750 / 11 )
= 25 days

Basic Formulas

• If a personA works twice as person B, then Ratio of work done by A and B is 2:1

 Example sum

A work can be finished in 16 days by twenty women. The same work can be finished in fifteen days by sixteen men.
Find the ratio between the capacity of a man and a woman?

Work done by 20 women in 1 day = 1 / 16
Work done by 1 woman in 1 day = 1 / ( 16*20)
Work done by 16 men in 1 day = 1 / 15
Work done by 1 man in 1 day = 1 / ( 15 *16)

The ratio of the capacity of a man and woman

= (1/(15*16)):(1/(16*20))

= (1/15):(1/20)

= (1/3):(1/4)

= 4:3

Basic Formulas

If ml men can do a work in dl days and m2 men can do the same work in d2 days, then 

(m1*d1)=(m2 *d2)

Example sum

12 men can do a work in 25 days. How long will 10 men take to complete the work?
ml = 12
dl = 25
m2=10
d2 = x

( m1*d1) = (m2*d2)

( 12*25)=(10*x)

x=( 12*25)/10
= 300/10
= 30
The required number of days = 30 days

Basic Formulas

A and B working together can do a piece of work in x days whereas B working alone can do the same work in y days. How
many days will A alone take to do the work?
(A+B)'s one day's work = l/x
B's one day's work = l/y
A alone will complete the work in ( xy / ( y-x)) days.

Example sum

A and B together can do a piece of work in 12 days, while B alone can finish it in 30 days. A alone can finish the work in:
A alone will complete the work in ( xy / ( y-x) )days.
x = 12
y = 30
A alone will complete the work = ( 12 * 30)/(30-12)

= (12*30)/18
=360/18
= 20
A alone will complete the work in 20 days