Sunday, 31 May 2015

07. Quantitative Aptitude Questions ---- Time and Work Solved Problems 2

                                 Aptitude Problems - Time and Work


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For solved problems on Time and work solved problems 1

Quantitative Aptitude – Time and Work Solved Problem 21
P can complete a piece of work in 18 days and B can do the same piece of work in 15 days. They started working together but after 3 days P left and Q alone completed the remaining work. The whole work was completed in (approximately)
a) 12.5 days          b) 8 days       c) 14 days          d) 14.5 days.     e)18 days
Answer: A
Explanation : Both together worked for 3 days.
 In 3 days , P can do = 3 x
1 / 18
  =
1 / 6
th work
In 3 days, Q can do =  3 x
1 / 15
=
1 / 5
th work
          In 3 days , work finished =
1 / 6
+
1 / 5
=
11 / 30
                    Balance work =
19 / 30
  Balance work finished by Q => Time taken by Q to finish the balance work =
19 / 30
x 15 = 9.5 days
The whole work was completed in 9.5 + 3 = 12.5 days.

Quantitative Aptitude – Time and Work Solved Problem 22
A can do a work in 36 days, B in 18 days and C in 24 days. B and C start the work but are forced to leave after 6 days. The remaining work was done by A in
a) 8 days           b) 9 days           c) 10 days     d) 12 days       e)15 days
Answer : E
Explanation :
In 6 days , B and C together finished => 6 x (
1 / 18
+
1 / 24
)
          = 6 x
7 / 72
   =
7 / 12
                  Balance work = 1-
7 / 12
=
5 / 12
  A can do complete work in 36 days.
    The remaining  5/12 th work done by A in =
5 / 12
X 36 = 15 days

Quantitative Aptitude – Time and Work Solved Problem 23
A can do a piece of work in 90 days and Y can do it in 80 days. They began working together  but A leaves after some days and then B completed  the remaining  work in 46 days. The number of days after which A left the work was
a) 15 days             b) 7 days                  c) 10days           d) 11 days         e)16 days
Answer: E
Explanation:  A and B did the work for some days.
After that , B completed the remaining work in 46 days .
In 46 days, word done by B =
1 / 80
  x 46 =
23 / 45
.
                Remaining work = 1 –
23 / 45
  =
17 / 45
Remaining work is done by both A and B together =
17 / 45
x
90 x 80 / 90 + 80
       = 16 days

Quantitative Aptitude – Time and Work Solved Problem 24
A is thrice as good a workman as B and therefore is able to finish a job in 45 days less than B. Working together,  they can finish the job in
a) 15 days              b) 11.25 days           c) 30 days       d) 45 days   e)60 days
Answer : B
Explanation :  A is thrice as good a workman as B =>A = 3B

 The ratio of efficiencies of A and B = 3:1
The ratio of the days taken by A and B to finish work is = 1: 3
                 B takes 45 days to finish the work => 3 parts = 45 days
                 A alone takes =>
45 / 3
x 1 = 15 days
  A and B alone can finish the work is =
AB / A+B
=
15 X 45 / 15 + 45
 
                                                                   = 11.25
                

Quantitative Aptitude – Time and Work Solved Problem 25
A woman can do a piece of work in 40 days. Man is 25% more efficient than Woman. The number of days taken by man to do the same piece of work is
a)12 days                b) 16 days     c) 25  days                   d) 32 days                   e)40 days
Answer :D
Explanation : The ratio of the efficiencies of a woman and man = 100 : 125
                  = 4 : 5
   The ratio of the days taken by woman and man to finish the work = 5 :4
                  Woman takes 32 days to finish the work.=> 5 parts = 40
       The number of days taken by man to finish the work = 4 parts =
40 / 5
x 4 = 32 days

Quantitative Aptitude – Time and Work Solved Problem 26
P is twice as good a workman as Q and Q is twice as good a workman as R. If A and B can together finish a piece of work in 6 days, then C can do it by himself in
a)10 days                b)8 days        c) 24 days               d)36 days     e)20 days
Answer: D
Explanation: Let P takes x days to finish the work, then Q takes 2x days and R takes 4x days.
Given A and B together finish the work in 6 days => In 1 day A+B can do
1 / 6
of the work
             In 1 day A and B together can do =>
1 / x
+
1 / 2x
=
1 / 6
    $\frac{3}{2x}$ = $\frac{1}{6}$
   => 2x=18  x=9
Therefore R can do the work in 4x = 4 x 9 = 36 days
                                  
Quantitative Aptitude – Time and Work Solved Problem 27
A takes twice as much time as B and C takes thrice as much time as B to finish a piece of work. Working together they can finish the work in 18 days. The number of days need for B to do the work alone is
a) 20 days               b) 22 days               c) 33 days     d)44 days        e)50 days
Answer:C
Explanation: Let A takes x days to complete the work , then B takes
x / 2
days and C takes
3x / 2
days to complete the work.
       A,B and C together complete the work in 18 days
In 1 day , all they together can do =>
1 / x
+
2 / x
+
2 / 3x
  =
1 / 18
ð  $\frac{3+6+2}{3x}$ =
1 / 18
ð  $\frac{3x}{2}$   = 18
ð  X = 66 days
The number of days B alone takes to finish the work =
x / 2
= 33 days

Quantitative Aptitude – Time and Work Solved Problem 28
A can do a work in 20 days, B can do it in 30 days, while C can do it in 12 days. In how many days will the work be completed if A and B  are assisted by C  on every third day?
a) 9 days                    b) 15 days       c) 18 days               d) 27 days     e)30 days
Answer:
Explanation : On every third day , A+B are assisted by C
In 1 day A and B together can do =
1 / 20
+
1 / 30
=  
5 / 60
=
1 / 12
    In 3 days A and B together can do = 3 x
1 / 12
=
1 / 4
work
  On 3rd day ,C assists A and B => In 3 days total work done =
1 / 4
+
1 / 12
=
4 / 12
=
1 / 3
                    In 3 days,
1 / 3
rd work will be completed
So Total work is completed in 3 x  3 = 9 days

Quantitative Aptitude – Time and Work Solved Problem 29
A and B can separately do a piece of work in 20 and 15 days, respectively. They worked together for 6 days, after which B was replaced by C. The work was finished in next 5 days. The number of days in which C alone could do the work is
a) 30 days               b) 45 days               c) 40 days               d) 35 days        e)50 days
Answer: E
Explanation : B worked for 6 days => In 6 days B completed = 6 x
1 / 15
2 / 5
th work
 A worked for  first 6 days and later 4 days => In 10 days A completed = 10 x
1 / 20
=
1 / 2
of the work
Total work done by A and B =
2 / 5
+
1 / 2
4+5 / 10
=
9 / 10
 Balance work = 1-
9 / 10
=
1 / 10
th of total work
 Balance work was completed by C in 5 days
         C can do 1/10 of the work in 5 days. Therefore C alone can do the work in 50 days.

Quantitative Aptitude – Time and Work Solved Problem 30
A and B together can complete a work in 15 days. A alone can complete in 20 days. If B does the work only 1/3rd of  a day daily, then in how many days A and B together will complete the work?         
 a) 10 days              b) 20 days               c) 11 days               d) 15 days     e)20 days
Answer: In 1 day, A+B can do =
1 / 15
th work   and A alone can do =
1 / 20
th of the work
    B alone can do the work in 1 day  , (A + B) – A =
1 / 15
1 / 20
           
4-3 / 60
=
1 / 60
th of the work
 B alone can do the work in 60 days.
If B works only
1 / 3
rd day => B alone can do the work in  3 x 60 = 180 days
Now In 1 day , A+B can do  =
1 / 15
+
1 / 180
   
                                      =   
(12+1) / 180
=
13 / 180
   A and B together will complete the work in
180 / 13
= 13
11 / 13
days if B does the work
1 / 3
rd day.

Quantitative Aptitude – Time and Work Solved Problem 31
A can do a work in 24 days, B in 12 days and C in 6 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in how many days?
a) 8 days          b) 6 days             c) 10 days                    d) 12 days     e)15 days
Answer:B
Explanation : In 1 day A can do
1 / 24
th of the work , B can do
1 / 12
th of the work and C can do
1 / 6
of the work
   In 3 days B completed  = 1/12  x 3 = ¼ th work
In 3 days C completed = 1/6 x 3  = ½ of the work
  In 3 days B and C completed = ¼ + ½ = ¾ th work
Balance work = 1 – ¾ = ¼ th work
The number of days A takes to complete the remaining work = ¼ x 24 = 6 days.

Quantitative Aptitude – Time and Work Solved Problem 32
A and B working separately can do a piece of work in 10 days and 15 days, respectively. If they work on alternate days beginning with A, in how many days will the work be completed?        
a) 18 days               b) 13 days               c) 12 days               d) 6 days      e)20 days
Answer:  C
Explanation : A and B can do
1 / 10
and
1 / 15
th work in a day.
They work on alternate days, beginning with A.
1ST day A works and on 2nd day B works.
In 2 days A+B can do =>
1 / 10
+
1 / 15
 
                        =  
5 / 30
=
1 / 6
th of the work.
In 2 days ,
1 / 6
th of the work will be completed.
Total work be completed in  6 x2 = 12 days


Quantitative Aptitude – Time and Work Solved Problem 33
A and B can do work in 18 and 24 days respectively. They together undertook a piece of work for Rs 4200, what is the share of A?
a)    Rs 1800             b)Rs 2400               c)Rs 2500                d)Rs 3000      e)Rs 3600
Answer : B
Explanation : The ratio of the days taken by A and B = 18 : 24  = 3 :4
    The ratio of the efficiencies of A and B = 4 :3
Wages are always distributed based the efficiencies of the people involved in the task.
      Share of A in total Rs 4200 remuneration = Rs 4200 x
4 / 7
= Rs 2400


Quantitative Aptitude – Time and Work Solved Problem 34
A can do a work in 36 days and B can do the same work in 48 days. With the help of C , they finished the work in 12 days. What is the share of C if their total remuneration is Rs 4800 ?
a)Rs 1800               b)Rs 600                 c)Rs 1200                d)Rs 2000      e)Rs 2500
Answer :C
Explanation : Wages are distributed in proportion to the part of the work done by each individual.
   A can do in 12 days =>
1 / 36
  x 12 =
1 / 3
rd work
  B can do in 12 days => 
1 / 48
x 12  =    
1 / 4
rth work
    A and B did = (
1 / 3
+
1 / 4
) =
7 / 12
th of the work
Remaining work done by C
 Remaining work = 1-
7 / 12
=
5 / 12
   Share of C in total remuneration Rs 4800 = Rs 4800 x
5 / 12
=Rs 2000

Quantitative Aptitude – Time and Work Solved Problem 35
A man and a boy received Rs 1600 as wages for 5 days for the work they did together. The man’s efficiency in the work was four times that of the boy. What are the daily wages of the boy?        
a) Rs 76                  b)Rs 56                   c) Rs 64                  d) Rs 40        e)Rs 50
Answer : C
Explanation : Man is 3 times efficient that of Boy => M = 4B
            Ratio of the efficiency of M and B   M:B= 4 :1
Wages are distributed in proportion to their efficiencies.
   Total wages of Boy = Rs 1600 x
1 / 5
= Rs 320
       Boy worked for 5 days , therefore daily wages of Boy = Rs
320 / 5
= Rs 64

Quantitative Aptitude – Time and Work Solved Problem 36
If 5 men or 7 women can earn Rs 10500 per day, how much would 7 men and 13 women earn per day?    
a) Rs 34200             b) Rs 31700             c) Rs 19500             d)Rs 17100      e)Rs 24000
Answer: A
Explanation: Daily earnings of 5 men = Rs 10500
              Daily earnings of 1 man =
10500 / 5
= Rs 2100
 Daily earnings of 7 women = Rs 10500
             Daily earnings of 1 woman =
10500 / 7
= Rs 1500
  Daily earnings of 7 men and 13 women = 7 x 2100 + 13 x 1500
        = 14700 + 19500 = Rs 34200

Quantitative Aptitude – Time and Work Solved Problem 37
A , B and C completed a work costing Rs 3600. A worked for 6 days, B worked for 4 and C worked for 9 days. If the ratio of the daily wages of A ,B and C are in the ratio 5 : 6 : 4, how much wages will be received by B ?
a)Rs 900                 b)Rs 720                 c)Rs 1080                d)Rs 960       e)Rs 1000
Answer:D
Explanation:  Ratio of the wages of A , B and C respectively = 5 x 6 :  6 x 4 : 4 x 9
                                                                                  = 30 : 24 : 36 = 5 : 4 : 6
    Therefore wages received by B = Rs  3600 x
4 / 5+4+6
                                               = Rs 3600 x
4 / 15
                                               = Rs 960

Quantitative Aptitude – Time and Work Solved Problem 38
1 man and 2 women together can complete a  work in 14 days while 4 men and 2 women together can do it in 8 days. If a woman gets Rs 1800 per day. How much should a man get per day ?
a)Rs 1200                b)RS 1400               c) Rs 1440               d)Rs 1500      e)Rs500
Answer : A
Explanation:   In 1 day 1M + 2W =
1 / 14
th work and 4 M +2 W =
1 / 8
th work
               14 M + 28 W = 1 and  32M + 16 W= 1
   Equating both  => 18 M = 12w =>  3 M = 2 W
                                  Therefore , 1 M =
2 / 3
W
       Amount received by 1 man per day = Rs  1800 x
2 / 3
= Rs 1200

Quantitative Aptitude – Time and Work Solved Problem 39
A, B and C  work for 7,8 and 10 days respectively and they together Rs 1440  for their work. If the ratio of their each day’s work is
1 / 3
:
1 / 4
:
1 / 6
; then how much does A get ?
a)Rs 720                 b) Rs 600                c)Rs 560        d)Rs 800                 e)Rs 400
Answer: B
Explanation:  The ratio of each day’s work =
1 / 3
:
1 / 4
:
1 / 6
        =   
4 / 12
  :
3 / 12
:
2 / 12
                                                           = 4 : 3 : 2
                  Ratio of the shares = 7 x4 : 8 x 3 : 10 x 2
                                           = 28: 24 : 20 = 7 : 6 : 5
   Share of A in the remuneration = Rs 1440 x
7 / 18
= Rs 560

Quantitative Aptitude – Time and Work Solved Problem 40
 A contractor engaged 5 men to complete a work in 20 days. After 15 days , he engaged 3 more men in order to complete the work on time. If additional men were not engaged , how many days  beyond the schedule it would have taken to complete the work ?
a)1 day                   b)2 days                 c)4 days                 d)5 days        e)3 days
Answer :E
Explanation : Total man days= Men x Days
          5 men worked for 15 days => Man days = 5 x 15 = 75 days
          Initial 5 men and additional 3 men worked remaining (20 – 15) =5 days =>
                              Man days  (5 +3) x 5 =40
          Total man days = 75 +40 = 115
If additional men not engaged , work done in = Number of man days / Number of Men
                                                               =
115 / 5
= 23

          Days beyond the schedule = 23 – 20 = 3 days

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