Time and Work: Aptitude Formulas, Problems & Tricks

Time & Work: It is one of the most important topic for aptitude exams like TCS placement test. Minimum 2-3 questions are always asked in aptitude tests from this topic.

Time & Work Aptitude Formulas:

1. If A can do a piece of work in n days, then A's 1 day's work = 1 / n.

2. If A's 1 day's work = 1 /n , then A can finish the work in n days.

3. Efficiency = Total work / Days 

4. If given the ratio of work is A:B , then ratio of the time taken will be B:A 

Q 1. Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long should it take both A and B, working together but independently, to do the same job?

Ans. 40 / 9 hours

A's 1 hour's work = 1/8

B's 1 hour's work = 1/10

(A+B)'s 1 hour's work = (1/8 + 1/10) = 9/40

9 / 40 work is done in = 1 hour
1 work will be done = 40 / 9 hours

Q 2. A can do a piece of work in 7 days of 9 hours each and B can do it in 6 days of 7 hours each. How long will they to do it , working together 42/5 hours a day?

Ans. 3 Days.

A can complete the work in 7 days of 9 hours each = 7x9 = 63 hours.
A's 1 hour;s work = 1/63
B can complete the work in 6 days of 7 hours each = 6x7 = 42 hours.
B's 1 hour's work = 1/ 42
(A+B)'s 1 hour's work = (1/63 + 1/42 ) = 5/126
So A and B finish the work in (126/5) hours.
Number of days of 42/5 hours each = (126/5 x 5/42) = 3 days.

Q 3. A and B can do a piece of work in 18 days, B and C can do it in 24 days , A and C can do it in 36 days. In how many days will A, B and C finish it,working together and separately?

Ans.

(A+B)'s 1 day's work = 1/18
(B+C)'s 1 day's work = 1/24
(A+C)'s 1 day's work = 1/36

Working  together:
Now adding , we get : 2(A+B+C)'s1 day's work = (1/18 + 1/24 + 1/36) = 9/72 = 1/8
(A+B+C)'s 1 day's work = 1/16
Thus A, B and C together can finish the work in 16 days.

Working separately:
A's 1 days work = [(A+B+C)'s 1 day's work] - [(B+C)'s 1 day's work]
                          = (1/16 - 1/24) = 1/48.
A alone can finish the work in 48 days.

B's 1 day's work = [(A+B+C)'s 1 day's work] - [(A+C)'s 1 day's work]
                           = (1/16 - 1/36) = 5/144.
B alone finish the work in 144/5 days.

C's 1 day's work = [(A+B+C)'s 1 day's work] - [(A+B)'s 1 day's work]
                           = (1/16 - 1/18) = 1/144.
C can alone finish the work in 144 days.

Q 4. 8 men can dig a pit in 20 days. If a man works half as much again as a boy, then 4 men and 9 boys can dig a similar pit in?

a. 10 days
b. 12 days
c. 15 days
d. 16 days

Ans. 16 Days.

Given that,
1 man = 3/2 boys (man works half as much again as a boy)
\So, (4 man + 9 boys ) = 15 boys.
Also, 8 men = 3/2 * 8 = 12 boys.
Now 12 men can dig the pit in 20 days.

15 boys can dig the pit in = 20 * 12 /15 = 16 days.

Q 5. A does half as much work as B in three-fourth of the time. If together they take 18 days to complete a work, how much time shall B take to do it ?
a. 30 days
b. 35 days
c. 40 days
d. None of these

Ans. 30 days.

 Suppose B takes x days to do the work.
A takes [2×34x] i.e., 3x2 days to do it.
Now (A + B)'s 1 day's work = 118
1x+23x=118 

or x=30 

Q 6. A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately. If A begins first, in how many days the work will be completed ?

a. 1012 days
b. 1014 days
c. 1023 days
d. 1013 days

Ans. B.

(A + B)'s 2 day's work = [19+112]=736
Evidently, the work done by A and B during 5 pairs of days = [5×736]=3536
Remaining work = [1−3536]=136
Now, on 11th day it is A's turn.
Now 19 work is done by A in 1 day.
136 work will be done by A in [9×136]=14 day
So, total time taken = 1014 days.

Q 7. A alone can finish a work in 10 days and B alone can do it in 15 days. If they work together and finish, then out of a total wages of Rs.75. A will get :
a. Rs.30
b. Rs.37.50
c. Rs.45
d. Rs.50

 Ans:  C.

Explanation

Ratio of time taken by A and B = 10 : 15 = 2 : 3
Ratio of work done in the same time  = 3:2, So, the money is to be divided among A and B in the ratio 3 : 2
A's share = Rs. [75×35] = Rs.45. 

Q 8. A, B and C together earn Rs.150 per day while A and C together earn Rs.94 and B and C together earn Rs.76. The daily earning of C is :

a. Rs.75
b. Rs.56
c. Rs.34
d. Rs.20

Ans.  Rs.20

B's daily earning = Rs.(150-94) = Rs.56
A's daily earning = Rs.(150-76) = Rs.74
C's daily earning = Rs.[(150-(56+74)] = Rs.20 

Q 9. A can complete a job in 9 days B in 10 days and C in 15 days. B and C start the work and are forced to leave after 2 days. The time taken to complete the remaining work is :

a. 6 days
b. 9 days
c. 10 days
d. 13 days

Ans. 6 days.

[B + C ]'s 2 days work = 2[110+115]=13
Remaining work = [1−13]=23
19 work is done by A in 1 day

23 work is done by A in [9×23]=6 days.

Q 10. 3 men and 4 boys do a piece of work in 8 days, while 4 men and 4 boys finish it in 6 days. 2 men and 4 boys will finish it in:

a. 9 days
b. 10 days
c. 12 days
d. 14 days

Ans. 12 days.
First method :
(3 men + 4 boys)'s 1 day's work = (18)
(4 men + 4 boys)'s 1 day's work = (16)
Subtracting :
1 man's 1 day's work = (16−18)=124
(2 men + 4 boys)'s 1 day, work = (18−124)=112
Thus, 2 men and 4 boys will finish it in 12 days.

Q 11. 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work?

Ans.

Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.

then, 

2x + 3y = 1/10and 3x + 2y = 1/8

Solving these equation we get 

x = 7/200 and y = 1/100

(2 men + 1 boy)'s 1 day's work = ( 2 * 7/200 + 1 * 1/100 ) = 16/200 = 2/25

So, 2 men and 1 boy together can finished the work in 25/2 days. 

Q 12. A completes a work in 4 days whereas B completes the work in 6 days. C works 112 times as fast as A. How many days it will take for the three together to complete the work ?
 
a. 712
b. 1512
c. 157
d. None of these
 
Ans.  D. Time taken by C alone = [23×4]=83 days
Their 1 day's work = [14+16+38]=1924
So, together they can finish the work in 2419 days i.e. 1519 days. 

Q 13. Twelve men can complete a work in 8 days. Three days after they started the work, 3 more men joined them. In how many days will all of them together complete the remaining work ?
 
a. 2
b. 4
c. 5
d. 6
 
Ans.  B.
 
 1 man's one day's work = 196
12 men's 3 day's work = [3×18]=38
Remaining work = [1−38]=58
15 men's 1 day's work = 1596 Now, 1596 work is done by them in 1 day,
58 work will be done by them in [9615×58] i.e.4 days

Q 14. . A, B and C contract a work for Rs.550. Together A and B are to do 711 of the work. The share of C should be
 
a. Rs.18313
b. Rs.200
c. Rs.300
d. Rs.400
 
Ans.  B.
Work to be done by C = [1−711]=411
(A + B) : C  = 711:411=7:4
C's share = Rs.[550×411] = Rs. 200

Q 15. Two men undertake to do a piece of work for Rs.400. One alone can do it in 6 days, the other in 8 days. With the help of a boy, they finish it in 3 days. The boy's share is
 
a. Rs.40
b. Rs.50
c. Rs.60
d. Rs.80
 
Ans. B.
One man's 1 day's work = 16
Another man's 1 day's work = 18
Boy's 1 day's work = 13−[16+18]=124
Ratio of their shares = 16:18:124 = 4:3:1
Boy's share = Rs. [400×18]=Rs.50

Q 16. If a man or 2 women or 3 boys can do a piece of work in 44 days, then the same piece of work will be done by 1 man, 1 woman and 1 boy in :
 
a. 21 days
b. 24 days
c. 26 days
d. 33 days

Ans. B.

1 man  = 2 women = 3 boys
1 woman = 12 man and 1 boy = 13 man
So, [1+12+13]men=[116men]
Now, 1 man can do the piece of work in 44 days
116men can do it in [44×611] = 24 days