# Aptitude  Time and Work  Theory

## Formula

• If A does a work in "a" days, then in one day A does $\dfrac{1}{a}$of the work.

If A can do a work in 10 days, in one day he can do 1/10th of the total work.

Simple! It can also be expressed in percentage
1/10*100 % or 10% of total work.

If A can do a work in 10 days, Then One day work of A = 1/10 of total work = 10% of total work.

Vice Versa, If A does 10% of work in day, he can complete the total work in 10 days.

• ## Solved Examples - Easy

• If 2 men can complete constructing a wall in 10 days, How many men are required to construct the wall in 5 days ?

As No of men increase, time Reduces. Work rate is inversely

proportional to time.

No of Days 2 x .

No of Men 10 5 .

In inverse proportion, No of days X No of men is a constant. 2 * 10 = 5*x

So x = 4 days

Alternate method: Total work = 20 man days

If 5 men are working, it will take (20 man days/5 man) = 4 days

• ## Work done - Formula

• Work done = Work Rate × Time
• ## Solved Examples - Easy

• If A can complete constructing a wall in 10 days, And B is three times efficient as A. How many days does B take to complete the job?

A's one day work = 1/10

B's one day work = 3 times A's work rate = 3/10

Applying formula = 1/10*10 = 3/10 * x

x = 3.33 days

Total work is taken as 1 unit of work, when the work done is same for tow cases.

• ## Working Together - Formula

• If A does a work in a days, then in one day A does A=$\dfrac{1}{a}$ of the work.

If B does a work in b days, then in one day B does B= $\dfrac{1}{b}$ of the work.

Then, in one day, if A and B work together, then their combined work is $\dfrac{1}{a}$ + $\dfrac{1}{b}$ or $\dfrac{a+b}{ab}$

• ## Solved Examples - 1

• 8 men can do a work in 12 days while 20 women can do it in 10 days. In how many days can 12 men and 15 women complete the same work.

Here man's one day work and women's one day work is known.

One Man's one day work =1/(8*12) = 1/96

One Women's one day work = (1/20*10) =1/200

If they work together

Total work done done by 12 men and 15 women = 12*(1/96) + 15 * (1/200) = 0.2 of the work = 20%

So to complete 100% work = 100/20 = 5 days

• ## Solved Examples - 2

• 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

Here man's one day work and women's one day work is known.

Let 1 mans 1 days work = x

1 womans 1 days work = y

Total work done by 4 men and 6 women in one day
= 4x + 6y = 1/8

Total work done by 3 men and 7 women in one day
= 3x + 7y = 1/10

x = 11/400 and y = 1/400 = 1 women's 1 day work

10 womens 1 days work = 10/400 = 1/40 of total work.

Hence 10 women will complete the work in 40 days.

• ## Solved Examples - 3

• P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 10 days. How many days more will P take to finish the work?

Let work done by P in 1 day = p,

Work done by Q in 1 day = q,

Work done by R in 1 day = r

p + q = 1/30

q + r = 1/24

r + p = 1/20

Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8

=> p + q + r = 1/16

=> Work done by P,Q and R in 1 day = 1/16

Work done by P, Q and R in 10 days = 10 × (1/16) = 10/16 = 5/8

Remaining work = 1 - 5/8 = 3/8

Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day

= 1/16 – 1/24 = 1/48

Number of days P needs to work to complete the remaining work = (3/8) / (1/48) = 18
•

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