**Time and Work-Key Notes**

**Time and Work-Key
Notes-aptitude-questions-answers-basics**

**Time and Work
Aptitude basics, practice questions, answers and explanations **

**Prepare for companies tests and interviews**

**Time & Work**

(M1D1HI)/ W1 = (M2D2H2)/W2

Where M1 & M2 represents no of labourers; D1 & D2 represents no of
days; H1 & H2 represents no of hours; W1&W2 represents work done.

If there are 2 persons A & B such
that A can do work in ?a? days and B can do work in ?b?days. Such that ?a? is a
multiple of ?b?, then, time taken by them to complete the work together =
Bigger no/Sum of ratios

Eg: A can do work in 9 days, B can do
work in 18 days. In how many days they will complete the work together.

Bigger no=18, Ratio=9:18=1:2

No of days = 18/(1 + 2)

= 6 days

If ?a? is not a multiple of ?b?, then
time taken by A&B to complete the work together

= (LCM)/(Sum of
ratios)

Eg: A can do a piece of work 30 days. B can do work in 45 days. In how many
days they will complete the work together?

LCM = 90, Ratio= 30:45=2:3

No of days= 90/(2 + 3) = 90/5 = 18

If there are 3 persons A, B & C
whose time taken a,b,c days respectively, to complete a certain work. Time
taken by them to complete the work = LCM of (a, b, c)/(LCM/a +
LCM/b + LCM/c)

Note: For 3 persons the common format is

Step1: Find the LCM

Step2: Find the individual share of work
i.e. LCM/a, LCM/b, LCM/c.

Step3: Rest methods depend on the
question i.e. follow the question patterns.

Eg: A, B and C can do a work in 15,20,45
days respectively. In how many days they can complete the work together.

LCM=180

No of days= [180/ (180/15 + 180/20 +
180/45)

= [180/
(12+9+4)]

= [180/25]

= 7.2 days

**Pipes & Cisterns**

If there are 2 pipes A & B such that
A (inlet pipe) & B (outlet pipe). Such that A can fill tank in ?a? minutes
and B can empty the tank in ?b? minutes , then time taken to fill the tank if
both are operated together = Bigger no/Difference of ratios

Eg: A can fill tank in 9 minutes, B can
empty the tank in 18 minutes.. In what time the tank be filled, if both pipes
work simultaneously?

Bigger no=18, Ratio=9:18=1:2

Time taken to fill the tank = 18/(2 - 1)

= 18 minutes

If ?a? is not a multiple of ?b?, then
time taken by A&B to fill the tank.

= (LCM)/(Difference
of ratios)

Eg.: An inlet pipe can fill the tank in 30 minutes. B an outlet pipe can empty
the tank in 45 minutes. In what time the tank be filled if both pipes work
simultaneously?

Time taken to fill the tank= LCM = 90

= Ratio= 30:45=2:3

= 90/(3 - 2) = 90/1 = 90 minutes

If there are 3 pipes A, B & C, in
which A, B are inlet pipes which takes a,b,minutes respectively to fill the
tank and C an outlet pipe which takes c minutes to empty the tank

Time taken by them to fill the tank, if
all of them are operated together.

= LCM of abc/ (LCM/a + LCM/b - LCM/c)

Eg: A, B two inlet pipes takes 15,18
minutes to fill the tank and C an oulet pipe takes 45 minutes to empty the tank
respectively. In what time the tank be filled if all of them are operated
together?

LCM=90

No of days= [90/(90/15 + 90/18 - 90/45)

=
[90/(6+5-2)]

= [90/9]

= 10 minutes

**Note:** In case of division of money
with respect to share of each person?s work then share of A = bc/ab+bc+ac

In case of division of money with
respect to share of each person?s work then share of B = ac/ab+bc+ac

In case of division of money with respect to share of each person?s work then
share of C = ab/ab+bc+ac

Same as Share of A:(LCM/a)/ (LCM/a +
LCM/b + LCM/c)

Share of B:(LCM/b)/ (LCM/a + LCM/b + LCM/c)

Share of C:(LCM/c)/ (LCM/a + LCM/b + LCM/c)

Eg: A,B,C can do a work in 15,20,45 days respectively. They get Rs 500 for
their work. What is the share of A?

LCM = 180

Share of A = (LCM/a x Total
amount)/LCM/a + LCM/b + LCM/c

= (180/15)/(180/15 +180/20 + 180/45)

= (12/25) * 500

= Rs.240

**Exercise questions**

1. Two workers A and B manufactured a
batch of identical parts. A worked for 2 hours and B worked for 5 hours and
they did half the job. Then they worked together for another 3 hours and they
had to do (1/20)th of the job. How much time does B take to complete the job,
if he worked alone?

A) 24 hours

B) 12 hours

C) 15 hours

D) 30 hours

2. Pipe A can fill a tank in 'a' hours.
On account of a leak at the bottom of the tank it takes thrice as long to fill
the tank. How long will the leak at the bottom of the tank take to empty a full
tank, when pipe A is kept closed?

A) (3/2)a
hours

B)
(2/3)a

C)
(4/3)a

D) (3/4)a

3. A and B working together can finish a
job in T days. If A works alone and completes the job, he will take T + 5 days.
If B works alone and completes the same job, he will take T + 45 days. What is
T?

A) 25

B) 60

C) 15

D) None of these

4. A man can do a piece of work in 60
hours. If he takes his son with him and both work together then the work is
finished in 40 hours. How long will the son take to do the same job, if he
worked alone on the job?

A) 0 hours

B) 120 hours

C) 24 hours

D) None of these

5. A, B and C can do a work in 5 days,
10 days and 15 days respectively. They started together to do the work but
after 2 days A and B left. C did the remaining work (in days)

A) 1

B)
3

C)
5

D) 4

6. X alone can do a piece of work in 15
days and Y alone can do it in 10 days. X and Y undertook to do it for Rs.720.
With the help of Z they finished it in 5 days. How much is paid to Z?

A) Rs.360

B) Rs.120

C) Rs.240

D) Rs.300

7. Ram starts working on a job and works
on it for 12 days and completes 40% of the work. To help him complete the work,
he employs Ravi and together they work for another 12 days and the work gets
completed. How much more efficient is Ram than Ravi?

A)50%

B) 200%

C) 60%

D)100%

8. A red light flashes 3 times per
minute and a green light flashes 5 times in two minutes at regular intervals.
If both lights start flashing at the same time, how many times do they flash
together in each hour?

A) 30

B)
24

C)
20

D) 60

9. A and B can do a piece of work in 21
and 24 days respectively. They started the work together and after some days A
leaves the work and B completes the remaining work in 9 days. After how many
days did A leave?

A) 5

B)
7

C)
8

D) 6

10. Ram, who is half as efficient as
Krish, will take 24 days to complete a work if he worked alone. If Ram and
Krish worked together, how long will they take to complete the work?

A) 16 days

B) 12 days

C) 8 days

D) 18 days

**Answer Key**

1.C; 2.A; 3.C; 4.B;5.D; 6.B; 7.D; 8.A;
9.B; 10.C