Tuesday, 16 June 2015

06. Quantitative Aptitude Questions- Time and Work Solved Problems 1

                                Aptitude Problems - Time and Work
For Better Understanding of this chapter Time and Work - Concept and Formulae

Quantitative Aptitude – Time and Work Solved Problem 1
30 men can do a work in 25 days. In how many days 20 men can do the same work ?
a)37.5 days             b)40 days                c)25 days                d)45 days      e)50 days
Answer:  A
Explanation: 30 men can do the work in 25 days.
   1 man can do the same  work in 30 x 25 days
   20 men will take =
(30 x 25) / 20
= 37.5 days

Quantitative Aptitude – Time and Work Solved Problem 2
A farmer can plough a filed working 10 hours day in 18 days. The farmer has to work how many hours per day to plough the same field in 12 days?
a)12 hours     b)12 hours              c)18 hours               d)15 hours     e)None of these
Answer : D
Explanation : 
Total hours to plough the field is 10 x 18 hours
                To finish in 12 days =>
(10 X 18) / 12
   = 15 hours

Quantitative Aptitude – Time and Work Solved Problem 3
64 men can do a piece of work in 30 days working 12 hours day. In how many days 80 men complete the same piece of work if they work for 16 hours a day ?
a)16 days      b) 18 days               c) 20 days               d)24 days      e)25 days
Answer :B
Explanation : 
M1 D1 H1 / W1
  =
M2 D2 H2 / W2
              Here W1=W2 because they all performing same piece of work.
          Here M1 = 64  D1= 30 and H1= 12   M2 =80    D2= ?  H2= 16   
                      M1D1H1 =  M2D2H2
                    64 x 30 x 12 = 80 X D2 X 16
            On solving, we get        D2 = 18 days

Quantitative Aptitude – Time and Work Solved Problem 4
If 120 men can build a wall of 104 meters long in 84 days for 8 hours a day , in how many days can 70 men build a similar wall of 52 meters long working for 9 hours a day ?
a)    64 days         b)40 days                c)50 days      d)56 days      e) 60 days
Answer : A
Explanation :            Here M1 = 120   D1= 84   H1= 8      W1= 104
   M2 =70      D2= ?    H2= 9  W2=  52
M1 D1 H1 / W1
=
M2 D2 H2 / W2
 
120 x 84 x 8 / 104
   =
70 x D2 x 9 / 52
On solving, we get D2= 64 days

Quantitative Aptitude – Time and Work Solved Problem 5
45 men can complete a work in 16 days. 7 days after they started working, 36 more men joined them. How many days will they now take to complete the remaining work?
a) 5 days                b) 8 days                c) 9 days       d)10.5 days             e)12 days
Answer:  A
Explanation:
Answer : M1=45 ,
    M2= 45 +36 = 81  (36 more men joined)
     D1= 16- 7 = 9 days  (4 days work is already done by 45 men)
D2 = ?
     M1D1 =M2 D2 
ð  45  x 9 = 81  X  D2 
ð  D2 = $ \frac{45\times9}{81} $ >
ð  D2 = 5 days  

Aptitude Questions – Time and Work Solved Problem 6
A road of 5 km length will be constructed in 80 days. So, 420 workers were employed. But after 60 days, it was found that only 3
1 / 2
km road was completed. Now, how many more people were needed to finish the work in the specified time?  
a) 480                    b)80             c) 200                    d)100            e)120
Answer:
Explanation: Total work is 5 km .   Work completed = 3 ½ =
7 / 2
km
                   Remaining work =
3 / 2
km
To finish in time , they have only 20 days ( 80 -60) to complete the balance work .( Because already 420 workers worked for 60 days)
  M1= 420     D1=60 W1=
3 / 5
km            M2= ? D2= 20         W2=
3 / 2
                      
M1 D1 / W1
=
M2 D2 / W2
ð  $\frac{420\times60}{7/2}$ = $\frac{M2\times20}{3/2} $
ð  420 x 60 x $ \frac{3}{2} $   = M2 X 20 X $\frac{7}{2} $
ð  M2=   
420 X 60 X 3 / 20 X 7
  
ð  M2 = 540
Required number of additional men = 540 – 420 = 120

Arithmetic Aptitude Questions – Time and Work Solved Problem 7
The typing speed of A and B together is 350 words in 5 minutes whereas A can type 200 words in 4 minutes. How many words can B type in 1 minute ?
a)10 word               b)20 words    c)30 words    d)40 words    e)50 words
Answer : B
Explanation : Together can type 35 words in 5 minutes =>In 1 minutes , they together can type
350 / 5
= 70 words per minute .
A along can type
200 / 4
= 50 words per minute.
   Therefore , B along can type 70 – 50 =  20 words per minute

Aptitude MCQ with Answers – Time and Work Solved Problem 8
Ramya takes 10 days to complete a piece of work and Radha takes 15 days to do the same work. In how many days they together will do the same work ?
a) 25 days             b) 20 days       c) 12 days      d) 8 days    e) 6 days
Answer : E
Explanation : In 1 day , ramya can do
1 / 10
th of the work
                     In 1 day ,Radha can do
1 / 15
th of the work
In 1 day , Ramya and Radha can do  (
1 / 10
+
1 / 15
) =
5 / 30
  =
1 / 6
th of the work
        So they both together can do the work in 6 days
Shortcut  :  If a A can do a work in A days and B can do in B days, the both together can do the work in AB/ A+B  days.
AB/ A+B   =>
10 x 15 / 10 +15
   = 6 days

Quantitative Aptitude Questions and Answers – Time and Work Solved Problem 9
A can do a job in 20 days. B takes 30 days and C finishes it in 60 days. If they all work together, how long will they take to complete the job ?
a) 9 days                      b)11.5 days   c)  12 days        d) 10 days               e)20 days
Answer: D
Explanation:  In 1 day, A can do
1 / 20
of the job, B can do
1 / 30
th of the job and C can do
1 / 60
th of the job.
Therefore in 1 day , A+B+C can do =
1 / 20
+
1 / 30
+
1 / 60
                 =
(3+2+1) / 60
=
1 / 10
th of the job
So A,B and C together can do the job  10 days

Aptitude Problems and answers – Time and Work Solved Problem 10
A and B take 12 days to do a piece of work, B and C take 15 days, C and A take 20 days. If A, B and C work together, they will complete the work in
a) 9  days               b) 18 days            c) 12 days            d) 16 days       e)20 days
Answer :C
Explanation : A+B can do
1 / 12
th of the work in a day , B+C can do
1 / 15
th of the work in a day and C+A  can do
1 / 20
th of the work in a day.
In 1 day  , (A+B) + (B+C) +(C+A) can do =
1 / 12
+
1 / 15
+
1 / 20
                                       2A+2B+2C     =
(5 + 4 + 3) / 60
                                         2(A+B+C)=
1 / 5
                                         A+B+C =
1 / 10
Therefore , A,B and C together can do the job in 10 days

Arithmetic Problems with Solutions – Time and Work Solved Problem 11
In the above problem , in how many days A alone can do the work ?
a)    30 days                  b)60 days      c)75 days      d)50 days      e)90 days
Answer :
Explanation :  In 1 day A alone can do = (A+B+C)’s 1 day work – (B+C)’s 1 day work
  (A+B+C )- (B+C)   =
1 / 10
1 / 15
   A =
(3-2) / 30
=
1 / 30
A alone can do the work in 30 days

Quantitative Aptitude Test Questions – Time and Work Solved Problem 12
A can do a piece of work in 5 days, but with the help of B, he can do it in 3 days. In what time can B do it alone ?
a) 8 days                       b) 6 days    c)   7
1 / 2
days                  d) 15 days e)20 days
Answer :
Explanation :  A with the help of B can do the work in 3 days .
               In 1 day (A+B) can do
1 / 3
of the work
               In 1 day A alone can do
1 / 5
of the work.
In 1 day  , B alone can do  (A+B)- A = 
1 / 3
1 / 5
                B =
5-3 / 15
=
2 / 15
th of the work
B alone can do
15 / 2
= 7 ½ days
Aptitude Questions and Answers – Time and Work Solved Problem 13
A can complete a piece of work in 16 days and B can do the same job in 12 days. With the help of C, they did the job in 4 days only. Then, C alone can do the job in :
a) 4 
4 / 5
days             b) 8
3 / 5
days   c) 9
3 / 5
days                d) 24 days    e)30 days
Answer :
Explanation : A and B with help of C, did the work in 4 days
 In 1 day (A+B+C) can do   =
1 / 4
th work
In 1 day (A+B) can do = (
1 / 16
+
1 / 12
)th of the work
  C alone can do in  1 day => (A+B+C) –(A+B) =
1 / 4
-(
1 / 16
+
1 / 12
)
ð   C = 12 – $ \frac{3+4}{48}$   => C =  5/48 th work
Therefore C alone can do the work in
48 / 5
= 9
3 / 5
days.

Quantitative Aptitude  Solved Questions– Time and Work Solved Problem 14
Soumya alone can do ¼ of the work  in 2.5 days and Sravani can do
1 / 3
of the work in 4 days.In how many days Soumya and Sravani working together will finish the work ?
a)    5 $ \frac{5}{11}$ days   b)6 days                 c)9 days        d)10 days      e)15 days
Answer :A
Explanation :
Soumya can do ¼ of the work in 2.5 days => Soumya can do the work in 4 x 2.5 = 10 days
Sravani can do
1 / 3
of the work in 4 days => Sravani can do the work in 3 x  4 = 12 days
     In 1 day , Soumya can do
1 / 10
th of the work
    In 1 day , Sravani can do
1 / 12
th of the work
  In 1 day , they both together can do  =>
1 / 10
+
1 / 12
=
11 / 60
   They both together can the work in
60 / 11
= 5 5/11 days


Arithmetic Word  Problems – Time and Work Solved Problem 15
 A and B can do a work in 15 days and 25 days respectively. A worked for 9 days and left the work .In how many B can complete the remaining work ?
a)    5 days          b)8 days        c)10 days                d)15 days      e)18 days
Answer: C
Explanation :   In 1 day A can do
1 / 15
th of the work
            In 9 days, A completed = 9 x
1 / 15
=
3 / 5
th of the work
 Balance work = 1 –
3 / 5
=
2 / 5
th of the work
B can complete the remaining
2 / 5
th work =
2 / 5
x 25 = 10 days

Arithmetic Aptitude Solved Questions– Time and Work Solved Problem 16
A can do a job in 48 days. He worked for 12 days and then B completed the remaining work in 30 days. In how many days A and B together can finish the work?
a)10 10/11 days       b)20 days      c)21 9/11 days         d)25 days      e)22 6/11 days
Answer :
Explanation : In 1 day , A can do
1 / 48
th work.
           In 12 days , A completed     12 x
1 / 48
=
1 / 4
of the work
  B completed remaining ¾ of the work in 30 days.
 B can do the complete work in  30 x
4 / 3
  = 40 days
      In 1 day , B can do
1 / 40
th work.
   In 1 day A and B together can do =
1 / 48
  +
1 / 40
                                                =  
(5 + 6) / 240
  =
11 / 140
     A and B together can do the work in
240 / 11
=  21
9 / 11
days

Quantitative Reasoning Solved Questions – Time and Work Solved Problem 17
20 men can do work in 30 days. 30 women can do it in 32 days. In how many days 10 men and 8 women can do the same work ?
a)20days                 b)25 days                c)28 days      d)40 days                e)15 days
Answer :
Explanation :
 20 men can do the work in  30 days
=> In 1 day , 1 man can do 
1 / 20 x 30
th of the work
30 women can do the work in 32 days
          => In 1 day, 1 woman can do
1 / 30 x 32
of the work.
In 1 day 10 men and 8 women can do => 10M + 8 W
= 10 X
1 / 20
X30  + 8 X
1 / 30
X 32
           = 
1 / 60
+
1 / 120
     = 
3 / 120
    10 M + 8 W can do the work in 
120 / 3
= 40 days

Aptitude Questions and Answers – Time and Work Solved Problem 18
16 men or 20 women can do a work in 30 days. In how many days 24 men and 10 women can do the same work ?
a)15 days                b)18 days                c)20 days                d)25 days      e)30 days
Answer : A
Explanation :   16 men can do the work in 30 days
=>In 1 day 1 man can do =
1 / 30 x 16
th work
20 women can do the work in 30 days
=> In 1 day, 1 woman can do =
1 / 20 x 30
th work

In 1 day 24 men and 10 women can do =
24 x
1 / 16 x 30
  + 10 x
1 / 20 x 30
                =
1 / 20
+
1 / 60
=
4 / 60
=
1 / 15
            24M + 10W can do the work in 15  days
 Aptitude Questions with Solutions– Time and Work Solved Problem 19
20men can do a job in 25days and 30 women can do the same in 35 days. What is the ratio between the capacities of a man and a woman ?
a)7:5                      b)5:7                      c)3:2                       d)2 :3           e)7 :10
Answer : A
Explanation : The number of days taken by 1 man to finish the work = 20 X 25 = 500
The number of the days taken by 1 woman to finish the work = 30 x 35 = 700
              Ratio of the days taken by 1 man and 1 woman = 500 : 700  = 5 :7
Ratio between the capacities of a man and a woman
 = Inverse ratio of the days taken by them = 7 :5

GMAT Word Problems  Aptitude – Time and Work Solved Problem 20
A can do a work in 12 days. When he had worked for 3 days, B joined him. If they complete the work in 3 more days, in how many days can B alone finish the work?
a) 6 days                b) 12 days               c) 4 days                 d) 8 days       e)10 days
Answer:
Explanation: In 3 days , A finished = 3 x
1 / 12
= ¼ th of the work
Remaining work is completed by both A and B in 3 days
 => Balance ¾ work completed by A+B together in 3 days =
3 / 4
W = 3 days =>W= 4 days
(A+B) can do the complete work in 4 days.
  In 1 day B can do => (A+B)- A =
1 / 4
  -
1 / 12
   =  3-
1 / 12
=
1 / 6

            B  alone can finish the work in 6 days.

For more problems on Time and Work , visit Time and Work Solved Problems 2
For more problems and online tests , visit http://www.9exam.com