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61. A can do a work in 10 days and B alone can do that work in 20 days. If B after doing 5 days leaves the job, find in how many days A will do the remaining work.
  A.  8.5 days
  B.  7.5 days
  C.  5.5 days
  D.  9.5 days
     
   
View Answer

Shortcut:
If X and Y can do a work in 'a' days and 'b' days respectively. Y leaves the work after working for 'z' days, then X will do the remaining work in
(b − z)a / b

Here, a = 10, b = 20, z = 5
Putting these values in the shortcut, we get:
Billu =
(20 − 5)10 / 20
=
15 x 10 / 20
= 7.5 days
Hence, Billu will do the work in 7.5 days.

62. 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.  4 days
  C.  7 days
  D.  5 days
     
   
View Answer

A's 1 day =
1 / 9
work
B's 1 day =
1 / 10
work
C's 1 day =
1 / 15
work
(B+C)'s 1 day work =
1 / 10
+
1 / 15
=
3 + 2 / 30
=
5 / 30
=
1 / 6

As per question (B + C) work for 2 days.
∴ (B + C)'s 2 days = 2 x
1 / 6
=
1 / 3
work
Remaining work = 1 −
1 / 3
=
2 / 3

Now,
2 / 3
work is to be done by A alone.
A does 1 work in 9 days
A does
2 / 3
work in 9 x
2 / 3
= 6 days.

63. A and B can do a piece of work in 10 days and 20 days. Both starts the work together for some time, but B leaves the job 7 days before the work is completed. Find the time in which work is finished.
  A.  6 days
  B.  7 days
  C.  8 days
  D.  9 days
     
   
View Answer

Shortcut:
X and Y can do a piece of work in 'a' and 'b' days respectively and both of them starts the work together. If Y leaves the work 'm' days before the completion of work, then the total time, in which the whole work is completed
(b + m)a / a + b

Here, a = 10, b = 20, m = 7
Putting these values in the shortcut, we get:
Required time =
(20 + 7)10 / 10 + 20
=
27 x 10 / 30
= 9 days
Hence, the work will finish in 9 days.

64. A and B can do a piece of work in 10 days and 15 days respectively. Both starts the work together but A leaves the work 5 days before its completion time. Find the time in which work is finished.
  A.  4 days
  B.  6 days
  C.  9 days
  D.  7 days
     
   
View Answer

Shortcut:
X and Y can do a piece of work in a and b days respectively and both of them starts the work together. If Y leaves the work 'm' days before the completion of work, then the total time, in which the whole work is completed
(a + m)b / a + b

Here, a = 10, b = 15, m = 5
Putting these values in the shortcut, we get:
Required time =
(10 + 5)15 / 10 + 15
=
15 x 15 / 25
= 9 days
Hence, the work will be finished in 9 days.

65. A can do a piece of work in 12 days. A does the work for 2 days only and leaves the job. B does the remaining work in 5 days. In how many days B alone can do the work?
  A.  4 days
  B.  6 days
  C.  5 days
  D.  8 days
     
   
View Answer

Shortcut:
X can do a piece of work in 'a' days. A does the work for 'm' days only and leaves the job. Y does the remaining work in 'n' days then Y can alone can do the work in
an / a − m
Here, a = 12, m = 2, n = 5
Putting these values in the shortcut, we get:
B =
12 x 5 / 12 − 2
=
12 x 5 / 10
= 6 days
Hence, B will finish in 6 days.

66. Raju completes a work in 10 days. Sunder completes the same work in 15 days. Raju starts working alone and after 5 days Biru joins him. How many days will they now take together to complete the remaining work?
  A.  6 days
  B.  5 days
  C.  3 days
  D.  4 days
     
   
View Answer

Shortcut:
X completes a work in 'a' days. Y completes the same work in 'b' days. A started working alone and after 'm' days Y joined him. Then the time in which, they will take together to complete the remaining work in
(a − m)b / a + b

Here, a = 10, b = 15, m = 5
Putting these values in the shortcut, we get:
Required time =
(10 − 5)15 / 10 + 15
=
5 x 15 / 25
= 3 days
Hence, both will finish the work in 3 days.

67. A completes a work in 12 days. B completes the same work in 15 days. A started working alone and after 3 days B joined him. How many days will they now take together to complete the remaining work?
  A.  4 days
  B.  7 days
  C.  6 days
  D.  5 days
     
   
View Answer

Shortcut:
X completes a work in 'a' days. Y completes the same work in 'b' days. A started working alone and after 'm' days Y joined him. Then the time in which, they will take together to complete the remaining work in
(a − m)b / a + b
Here, a = 12, b = 15, m = 3
Putting these values in the shortcut, we get:
Required time =
(12 − 3)15 / 12 + 15
=
9 x 15 / 27
= 5 days
Hence, both will finish in 5 days.

68. 10 men and 15 women finish a work in 6 days. One man alone finished that work in 100 days. In how many days will a woman finish the work?
  A.  215 days
  B.  225 days
  C.  235 days
  D.  220 days
     
   
View Answer

1 man alone finishes the work in 100 days.
∴ 10 men finish the work in 10 days.
From the question,
15 women finish in 1 day =
1 / 6
-
1 / 10
=
1 / 15
work
∴ 15 women finish the whole work in 15 days.
∴ 1 women finishes the whole work in 15 x 15 = 225 days.

69. Raj can finish a job in 20 days. He worked for 10 days alone and completed the remaining job working with Deepu, in 2 days. How many days would both Deepu and Raj together take to complete the entire job?
  A.  4 days
  B.  3 days
  C.  5 days
  D.  6 days
     
   
View Answer

Raj alone finished
1 / 2
of the work in 10 days.
Remaining
1 / 2
of the job was finished by Raj and Deepu together in 2 days.
∴ they both together can finish the job in 4 days.

70. A can do a piece of work in 12 days. B is 60% more efficient than A. The number of days, it takes B to do the same piece of work are:
  A.  5
1 / 2
days
  B.  7
3 / 2
days
  C.  7
1 / 2
days
  D.  5
3 / 2
days
     
   
View Answer

A's 1 day work =
1 / 12

B's 1 day work =
1 / 12
+ 60% of
1 / 12
=
2 / 15

∴ B can do the work in
15 / 2
ie 7
1 / 2
days.

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