QUANT QUIZ ( TIME AND WORK WITH ANSWER & EXPLANATION )

1.    A and B
together can do a piece of work in 30 days. A having worked for 16 days, B
finishes the remaining work alone in 44 days. In how many days shall B finish
the whole work alone?
(1) 40days                         (2) 30
days
(3)
60 days          
            (4)
50 days


2.    A and B can do a job together in 7
days. A is 1  3 /4 times as
efficient as B. The same job can be done by A alone in :
(1) 12 days                        (2) 11 days
(3) 15 days                        (4) 16 days

3.    X can do a piece of work in 40 days.
He works at it for 8 days and then Y finished it in 16 days. How long will they
together take to complete the work?
(1) 13 1/3 days                  (2)15 days
(3)16 days                         (4) 17 days

4.    A can finish a work in 24 days, B in 9
days and C in 12 days. B and C start the work but are forced to leave after 3
days. The remaining work was done by A in:
(1) 15 days                        (2) 10 days
(3) 12 days                        (4) 14 days

5.    A and B can do a work in 8 days, B and
C can do the same work in 12 days. A, B and C together can finish it in 6 days.
A and C together will do it in :
(1) 4 days                          (2) 8
days
(3) 6days                           (4) 7
days

6.    Twenty women can do a work in sixteen
days. Sixteen men can complete the same work in fifteen days. What is the ratio
between the capacity of a man and a woman?
(1) 4 : 3                              (2) 3: 4
(3) 5 : 3                              (4)
 3: 5

7.    A works twice as fast as B. If B can
complete a work in 12 days independently, the number of days in which A and B
can together finish the work in :
(1) 4 days                          (2)
8 days
(3) 2 days                          (4) 5
days

8.    A and B can complete a work in 15 days
and 10 days respectively. They started doing the work together but after 2 days
B had to leave and A alone completed the remaining work. The whole work was
completed in :
(1) 16 days                        (2) 14 days
(3) 18 days                        (4) 12 days

9.    A takes twice as much time as B or
thrice as much time as C to finish a piece of work. Working together, they can
finish the work in 2 days. B can do the work alone in:
(1) 6 days                          (2) 12 days
(3) 8 days                          (4)7
days

10.  Sakshi can do a piece of work in 20
days. Tanya is 25% more efficient than Sakshi. The number of days taken by
Tanya to do the same piece of work is
(1) 8 days                          (2) 15
days
(3) 16 days                        (4) 13
days

ANSWERS

1.    (3) 
Explanation:
Let
A’s 1 day’s work = x and B’s 1 day’s work = y.
Both A’s and B’s 1 day work=1/30
i.e (A’s 1 day + B’s 1 day)=1/30
i.e x + y = 1/30……..eq1
now,
A having worked for 16 days, B finishes the remaining work alone in 44 days
i.e work done by A in 16 days = 16x
Remaining work done B= 1 – 16x
but Remaining work is done by B in 44days i.e 44y
i.e. 44y=1-16x
i.e 16x+44y=1……..eq2
solving eq1 & eq2,
we get,x = 1/60 and y = 1/60
B’s 1 day’s work = 1/60.
Hence, B alone shall finish the whole work in 60 days.

2.    (2)
Explanation:
(A’s
1 day’s work) : (B’s 1 day’s work) = 7 /4 : 1 =  7 : 4
Let
A’s and B’s 1 days’ work  be 7 x and 4 x
respectively
then
, 7x + 4 x= 1/7 
à 11 x = 1/7  à x = 1/77
A’s  1 days = 1 / 77 x 7 = 1/ 11
Hence, A alone shall finish the whole work in 11 days.
3.    (1)
Explanation:
Work
done by X in 8 days = ( 1 / 40 x 8 ) = 1/5
Remaining
work ( 1  – 1/ 5 )  = 4/ 5
Now,
4/ 5 work is done by Y in 16 days
Whole
work will be done by Y in ( 16 x 5 / 4 ) = 20 
days
So,  X’s 1 days work = 1/ 40 , Y’s 1 day’s work =
1 / 20 
(
X+ Y )’s 1  days’ work  = ( 1/ 40 
+ 1/ 20 ) = 3 / 40
Hence
, X and Y  will together complete the
work in  ( 40 / 3) = 13  1/ 3 days

4.    (2)
Explanation:
Total
Unit of work=LCM(Time taken by A,Time taken by B,Time taken by
c)=LCM(24,9,12)=72
A’s 1 day work=72/24=3unit
B’s 1 day work=72/9=8 unit
C’s 1 day work=72/12=6unit
work done by(B+C) in 1 day=(8+6)unit=14 unit
work done by(B+C) in 3 day=14×3=42 unit
Remaing work=(Total work – work done by B+C in 3 days)= (72-42)=30unit
Remaing work done by A in=Remaining work/A’s 1 day work= 30/3=10 days

5.    (2)
Explanation:
(A+B+C)=1/6
A’s one day work work= (A+B+C)-(B+C)= 1/6-1/12 =1/12
C’s one day work work= (A+B+C)-(A+B)= 1/6-1/8= 1/24
(A+C)’s one day work= 1/12+1/24= 1/8
so the work will be completed in 8 days

6.    (1)
Explanation:
(20
x 16) women can complete the work in 1 day
1
woman’s 1 day’s work = 1/ 320
16
x 15) men can complete the work in 1 day
1
man’s 1 day’s work = 1/240
required
ratio =1/240:1/320.
Now (1/240)/(1/320).
By solving:
(1/240)*(320/1)
=320/240
=4/3 i.e. 4:3.

7.    (1)
Explanation:
B’S
one day work=1/12
A’S one day work=2(1/12)=1/6
(A+B) one day work=(1/12)+(1/6)=1/4
hence A and B together complete the work in 4 days

8.    (4)
Explanation:
A’s
1 day work=1/15
B’s 1 day work=1/10
now,B left after 2 days then 1/10*2=1/5
remaining work is (1-1/5)=4/5
4/5 work is left by B then A has to do remaining work (1/15*5/4)=1/12 this is
A’s 1 day work after B left work
now A completes work in 12 days…

9.    (1)
Explanation:
A
takes twice much time them B i.e. 2A=B…(i)
A takes thrice much time thn C i.e. 3A=C…(ii)
It is given dat workin together they can finish in 2 days
so A+B+C=1/2
Now put B=2A AND C=3A in this equ…
A+B+C=1/2
A+2A+3A=1/2
6A=1/2
A=1/2*6=1/12
Now put the value of A in equ.(i)
.i.e B=2A
=2*1/12
=1/6
Therefore B takes 6 days to complete the work.

10.  (3)
Explanation:
Tanya
is 25% more efficient than Sakshi.
Tanya is 125.
Sakshi is 100.
Ratio of efficiency is 5:4.
So, ratio of time will be 4:5.
Given, Sakshi can do work in 20 days means 5*4=20.
In the same way for Tanya 4*4=16.