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1. 20 men can do a piece of work in 10 days. How many men are needed to complete the work in 50 days?
  A.  4 Men
  B.  8 Men
  C.  5 Men
  D.  3 Men
     
   
View Answer

Shortcut:
If M1 men can do W1 work in D1 days and M2 men can do W2 work in D2 days then their relationship is given by
M1D1W2 = M2D2W1
Here, M1 = 20, D1 = 10, W1 = 1, M2 = ?, D2 = 50, W2 = 1
Using these values in the shortcut, we get:
20 x 10 = M2 x 50
∴ M2 =
20 x 10 / 50
= 4
Hence, 4 men are needed to complete the work in 40 days.

2. 40 men can cut 60 trees in 8 hours. If 8 men leave the job, how many trees will be cut in 12 hours?
  A.  82 trees
  B.  75 trees
  C.  72 trees
  D.  70 trees
     
   
View Answer

Shortcut:
If M1 men can do W1 work in D1 days and M2 men can do W2 work in D2 days then their relationship is given by
M1D1W2 = M2D2W1
Here, M1 = 40, D1 = 8, W1 = 60, M2 = 32 (40 − 8), D2 = 12, W2 = ?
Using these values in the shortcut, we get:
40 x 8 x W2 = 32 x 12 x 60
∴ W2 =
32 x 12 x 60 / 40 x 8
=
32 x 12 x 6 / 4 x 8
= 72
Hence, 72 trees will be cut in 12 hours.

3. A can do a piece of work in 5 days. How many days will he take to complete 3 works of the same type?
  A.  10 days
  B.  15 days
  C.  14 days
  D.  None of the above
     
   
View Answer

Shortcut:
If M1 men can do W1 work in D1 days and M2 men can do W2 work in D2 days then their relationship is given by
M1D1W2 = M2D2W1
Here, M1 = M2 = 1, D1 = 5, W1 = 1, D2 = ?, W2 = 3
Using these values in the shortcut, we get:
5 x 3 = D2 x 1
∴ D2 = 15
Hence, he will take 15 days.

4. 5 men can prepare 10 toys in 6 days working 6 hours a day. Then in how many days can 12 men prepare 16 toys working 8 hours per day?
  A.  9 days
  B.  6 days
  C.  3 days
  D.  5 days
     
   
View Answer

Shortcut:
If M1 men can do W1 works in D1 days working T1 hours a day and M2 men can do W2 work in D2 days working T2 hours a day then their relationship can given by
M1D1 T1W2 = M2D2T2W1
Here, M1 = 5, D1 = 6, T1 = 6, W2 = 16
M2 = 12 D2 = ?, T2 = 8, W1 = 10
Using these values in the shortcut, we get:
5 x 6 x 6 x 16 = 12 x D2 x 8 x 12
D2 =
5 x 6 x 6 x 16 / 12 x 8 x 12
= 3
Hence, he will take 3 days.

5. The work done by a woman in 8 hours is equal to the work done by a man in 6 hours and by a boy in 12 hours. If working 6 hours per day 9 men can complete a work in 6 days then in how many days can 12 men, 12 women and 12 boys together finish the same work working 8 hours per day?
  A.  3
1 / 2
days
  B.  2
3 / 2
days
  C.  1
3 / 2
days
  D.  1
1 / 2
days
     
   
View Answer

Shortcut: If M1 men can do W1 works in D1 days working T1 hours a day and M2 men can do W2 work in D2 days working T2 hours a day then their relationship can given by M1D1 T1W2 = M2D2T2W1
Here, 8 women = 6 men = 12 boys
8 women = 6 men
1 women =
6 / 8
men or
3 / 4
men
12 women =
3 / 4
x 12 = 9 men
Similarly, 12 boys = 6 men
1 boy =
6 / 12
men or
1 / 2
men
12 boys =
1 / 2
x 12 = 6 men
12 Men + 12 Women + 12 Boys = 12 Men + 9 Men + 6 Men = 27 Men
T1 = 6, M1 = 9, D1 = 6, W2 = 1
T2 = 8, M2 = 27, D2 = ?, W1 = 1
Using these values in the shortcut, we get:
9 x 6 x 6 = 27 x 8 x D2
D2 =
9 x 6 x 6 / 27 x 8
=
3 / 2
= 1
1 / 2

Hence, they will take 1
1 / 2
days.

6. A and B can do a piece of work in 12 days, B and C in 15 days, C and A in 20 days. How long would each take separately to do the same work?
  A.  A = 20 days, B = 30 days, C = 40 days
  B.  A = 30 days, B = 20 days, C = 60 days
  C.  A = 40 days, B = 50 days, C = 30 days
  D.  A = 50 days, B = 40 days, C = 20 days
     
   
View Answer

Shortcut:
If P and Q can do a piece of work in x days, Q and R in y days, R and P in z days, then (P + Q + R) working together will do the same work in
2xyz / xy + yz + zx
days.
Let we denote t =
2xyz / xy + yz + zx
then
P alone will do the same work in
yt / y − t
days
Q alone will do the same work in
zt / z − t
days
R alone will do the same work in
xt / x − t
days
Here, x = 12, y = 15, z = 20
Using these values in the shortcut, we get:
t =
2 x 12 x 15 x 20 / 180 + 300 + 240
=
2 x 12 x 15 x 20 / 720
= 10
Hence, A + B + C will take 10 days.
Now, A can do the work in
10 x 15 / 15 − 10
= 30 days
Now, B can do the work in
10 x 20 / 20 − 10
= 20 days
Now, C can do the work in
10 x 12 / 12 − 10
= 60 days

7. A and B can do a piece of work in 10 days, B and C in 15 days and C and A in 20 days. They all work at it for 6 days, and then A leaves, and B and C go on together for 4 days more. If B then leaves, how long will C take to complete the work?
  A.  8 days
  B.  12 days
  C.  10 days
  D.  None of the above
     
   
View Answer

Shortcut:
We know, A, B and C together will do work in
2xyz / xy + yz + zx
days
x = 10, y = 15, z = 20
A, B and C together can do the work in
2 x 10 x 15 x 20 / 10 x 15 + 20 x 10 + 15 x 20

=
2 x 10 x 15 x 20 / 150 + 200 + 300

=
2 x 10 x 15 x 20 / 650

=
2 x 10 x 3 x 2 / 13
=
120 / 13
days
Work done by all in 6 days =
13 / 20

Work done by B and C in 4 days =
4 / 15

Remaining work = 1 −
(
13 / 20
+
4 / 15
)
=
1 / 12
(This work is to be done by C)
Now from the question
C alone can do the whole work in =
(120/13) x 10 / 10 − 120/13
=
1200/13 / (130 − 120)/13
=
1200 x 13 / 13 x 10
= 120 days
∴
1 / 12
of the work is done by C in
120 / 12
days i.e. 10 days

8. A can do a piece of work in 5 days, and B can do it in 6 days. How long will they take if both work together?
  A.  2
8 / 11
days
  B.  3
11 / 8
days
  C.  2
1 / 11
days
  D.  2
9 / 11
days
     
   
View Answer

Shortcut:
If P can do a piece of work in x days and Q can do it in y days then P and Q working together will do the same work in
xy / x + y
days.
Here, x = 5, y = 6
Using these values in the shortcut, we get:
=
5 x 6 / 5 + 6
=
30 / 11
= 2
8 / 11
days
Hence, they all together will take 2
8 / 11
days

9. A can do a piece of work in 6 days. B takes 8 days. C takes as long as A and B would take working together. How long will it take B and C to complete the work together?
  A.  1
6 / 5
days
  B.  2
3 / 5
days
  C.  3
1 / 5
days
  D.  2
2 / 5
days
     
   
View Answer

Shortcut:
If P can do a piece of work in x days and Q can do it in y days then P and Q working together will do the same work in
xy / x + y
days.
Here, x = 6, y = 8
A and B all together will take
6 x 8 / 6 + 8
=
48 / 14
=
24 / 7
days
Hence, according to the question C will take
24 / 7
days
∴ B and C together complete the work in
=
8 x 24/7 / 8 + 24/7
=
12 / 5
= 2
2 / 5

Hence, they all together will take 2
2 / 5
days.

10. A does
7 / 10
days of a piece of work in 15 days. He does the remainder with the assistance of B in 4 days. In what time could A and B together do it?
  A.  13
1 / 4
days
  B.  13
1 / 3
days
  C.  3
1 / 13
days
  D.  12
5 / 3
days
     
   
View Answer

Shortcut:
If P can do a piece of work in x days and Q can do it in y days then P and Q working together will do the same work in
xy / x + y
days.
A does
7 / 10
work in 15 days.
Remaining work =
(
1 −
7 / 10
)
=
3 / 10

Now,
3 / 10
work is done by A and B in 4 days
∴ The whole work is done by A and B in
4 x 10 / 3
=
40 / 3
= 13
1 / 3
days
Hence, they all together will take 13
1 / 3
days.

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