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21. If factory A turns out m bikes an hour and factory B turns out n bikes every 2 hours, the number of bikes which both factories turn out in 8 hours is:
  A.  (2m + n)4
  B.  (2m + n)3
  C.  (m + 2n)4
  D.  (2m + n)2
     
   
View Answer

Factory A turns out bikes in 1 hour = m
Factory B turns out bikes in 1 hour = n/2
Factories (A + B) turn out bikes in 1 hour = m +
n / 2
=
2m + n / 2

Factories (A + B) turn out bikes in 8 hours = 8 x
2m + n / 2
= 4(2m + n)
Hence, both factories will turn out 4(2m +n) bikes in 8 hours.

22. 12 men can complete a work within 9 days. After 3 days they started the work, 6 men joined them to replace 2 men. How many days will they take to complete the remaining work?
  A.  3
1 / 2
days
  B.  4
1 / 2
days
  C.  4
3 / 2
days
  D.  3
1 / 3
days
     
   
View Answer

12 men can complete
1 / 3
of work in 3 days and the remaining
2 / 3
work in 6 days.
1 man can complete
2 / 3
work in (12 x 6) = 72 days.
∴ 12 − 2 + 6 = 16 mn can complete
2 / 3
work in
72 / 16
= 4
1 / 2
days

23. A can do a piece of work in 5 hours. B in 9 hours and C in 15 hours. If C could work with them for 1 hour only, the time taken by A and B together to complete the work is:
  A.  1 hours
  B.  2 hours
  C.  3 hours
  D.  4 hours
     
   
View Answer

A's work in 1 hour =
1 / 5

B's work in 1 hour =
1 / 9

C's work in 1 hour =
1 / 15

(A + B)'s work in 1 hour =
1 / 5
+
1 / 9
=
(9 + 5) / 45
=
14 / 45

(A + B + C)'s work in 1 hour =
1 / 5
+
1 / 9
+
1 / 15
=
(9 + 5 + 3) / 45
=
17 / 45

Remaining work = 1 −
17 / 45
=
(45 − 17) / 45
=
28 / 45

28 / 45
work is to be done by (A + B) only
14 / 45
work is done by (A + B) in 1 hour
1 work is done by (A+B) in
45 / 14
hour
28 / 45
work is done by (A+B) in
28 / 45
x
45 / 14
= 2 hours

24. Two workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3 as efficiently as he actually did, the work would have completed in 3 days. Find the time for A to complete the job alone.
  A.  6
1 / 4
days
  B.  5
1 / 4
days
  C.  6
1 / 3
days
  D.  5
1 / 2
days
     
   
View Answer

Efficiency is proportional to work done per day and work done per day x number of days worked = Amount of work done.
Considering efficiency of A and B initially as 1.
Let A alone can do the work in 'a' days and B alone can do the same work in 'b' days
Then,
5 / a
+
5 / b
= total work done = 1
Since efficiency of A and B are 2 and
1 / 3
respectively.
∴
(
1 / a
x 2 x 3
)
+
(
1 / b
x
1 / 3
x 3
)
= 1
or,
6 / a
+
1 / b
= 1 ...............(eq 1)
1 / a
+
1 / b
=
1 / 5
..............(eq 2)
Now, subtracting eq 1 from eq 2, we get:
a =
25 / 4
= 6
1 / 4
days.

25. 15 men would finish a piece of work in 210 days. But at the end of eveyr 10 days, 15 additional men are employed. In how many days will it be finished?
  A.  50 days
  B.  60 days
  C.  65 days
  D.  70 days
     
   
View Answer

10 days work by 15 men =
10 / 210
=
1 / 21

At the end of every 10 days 15 additional men are employed i.e for the next 10 days we have 15 + 15 = 30 men
∴ Next 10 day's work by 30 men =
2 / 21

Hence, in 20 days only
(
1 / 21
+
2 / 21
=
3 / 21
)
work is completed.
To complete the whole work we have to reach the value of
21 / 21
work.
Now,
1 / 21
+
2 / 21
+
3 / 21
+ ....
6 / 21
=
21 / 21
= 1
Hence, total time to complete the whole work = 10 + 10 + 10 + 10 + 10 = 60 days

26. A can copy 75 pages in 25 hours. A and B together can copy 135 pages in 27 hours. In what time can B copy 42 pages?
  A.  21 hours
  B.  20 hours
  C.  22 hours
  D.  23 hours
     
   
View Answer

In 25 hours A can copy 75 pages.
In 1 hour A can copy
75 / 25
= 3 pages
In 27 hours, A and B can copy 135 pages
In 1 hour A and B can copy
135 / 27
= 5 pages
∴ In 1 hour B can copy (5 − 3 = 2) pages
∴ B can copy 42 pages in 21 hours.

27. A completes a work in 15 days. B completes the same work in 20 days. A started working alone and after 1 day B joined him. How many days will they now take together to complete the remaining work?
  A.  5 days
  B.  6 days
  C.  7 days
  D.  8 days
     
   
View Answer

A's 1 day work =
1 / 15

B's 1 day work =
1 / 20

(A + B)'s 1 day work =
1 / 15
+
1 / 20
=
4 + 3 / 60
=
7 / 60

Remaining work = 1 −
1 / 15
=
14 / 15

14 / 15
work is to be done by (A + B)
7 / 60
work is done in = 1 day
1 work is done in =
60 / 7
day
14 / 15
work is done in =
14 / 15
x
60 / 7
= 2 x 4 = 8

28. 12 men take 18 days to complete a job whereas 12 women in 18 days can complete
3 / 4
of the same job. How many days will 10 men and 8 women together take to complete the same job?
  A.  12
1 / 2
days
  B.  13
1 / 3
days
  C.  13
1 / 2
days
  D.  12
1 / 3
days
     
   
View Answer

12 M x 18 = 12 W x 18 x
4 / 3

∴ W =
3 / 4
M
10M + 8W = 10M + 8 x
3 / 4
M = 16M
∴ 16 men can complete the same work in
12 x 18 / 16
=
27 / 2
= 13
1 / 2

Hence, they will take 13
1 / 2
days to complete the remaining work.

29. A and B can do a pice of work in 22 days and 23 days respectively. They start the work together but after some days, A leaves the job. B alone does the remaining work in 8 days. Find after how many days does A leave the job?
  A.  6
1 / 3
days
  B.  7
1 / 3
days
  C.  8
1 / 2
days
  D.  7
1 / 2
days
     
   
View Answer

Shortcut:
X and Y cn do a piece of work in 'a' and 'b' days respectively. Both starts the work together. But after some time X leaves the work and Y does the remaining work in 'z' days, then the time after which A leaves the work is
(b − z)a / a + b

Here, a = 22, b = 23, z = 8
Using these values in the shortcut, we get:
=
(23 − 8)22 / 22 + 23
=
15 x 22 / 45
=
22 / 3
= 7
1 / 3

Hence, A left the work after 7
1 / 3
days.

30. A can do a piece of work in 22 days. A does the work for 12 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.  11 days
  B.  10 days
  C.  12 days
  D.  13 days
     
   
View Answer

Shortcut:
X can do a piece of work in 'a' days. If X does the work only for 'm' days and the remaining work is done by Y in 'n' days, the Y alone can do the work in
an / a − m

Here, a = 22, m = 12, n = 5
Using these values in the shortcut, we get:
=
22 x 5 / 22 − 12
=
22 x 5 / 10
= 11 days
Hence, B alone can do the work in 11 days.

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