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31. If 12 women and 16 girls can do a piece of work in 5 days and 13 women and 24 girls can do it in 4 days, how long will 7 women and 10 girls take to do it?
  A.  6
1 / 3
days
  B.  8
1 / 3
days
  C.  8
2 / 3
days
  D.  6
2 / 3
days
     
   
View Answer

Shortcut:
If a1 men and b1 women can do a piece of work in x days and a2 men and b2 women can do it in y days, then
1 man =
yb2 − xb1 / xa1 − ya2
women
Here, a1 = 12, b1 = 16, x = 5, a2 = 13, b2 = 24, y = 4
Using these values in the shortcut, we get:
1 Woman =
4 x 24 − 5 x 16 / 5 x 12 − 4 x 13
=
96 − 80 / 60 − 52
=
16 / 8
= 2 girl
Thus 12 women + 16 girls = 24 girls + 16 girls = 40 girls
and 7 women + 10 girls = 14 girls + 10 girls = 24 girls
Now, by basic formula, we get
40 x 5 = 24 x D2
or D2 =
40 x 5 / 24
= 8
1 / 3
days
Hence, they will take 8
1 / 3
days.

32. 8 children and 12 men complete a certain piece of work in 9 days. Each child take twice the time by a man to finish the work. In how many days will 12 men finish the same work?
  A.  10 days
  B.  11 days
  C.  12 days
  D.  13 days
     
   
View Answer

2 children = 1 man
∴ 8 children + 12 men = 16 men
From the question,
Since 16 men can complete a certain piece of work in 9 days.
∴ 12 men finish the work in
16 x 9 / 12
= 12 days
Hence, they will finish the same work in 12 days.

33. A certain number of boys can do a work in 50 days. If there were 8 boys less it could be finished in 10 days more. How many boys are there?
  A.  42 boys
  B.  46 boys
  C.  48 boys
  D.  52 boys
     
   
View Answer

Shortcut:
A certain number of men can do a work in 'Z' days. If there were 'a' men less it could be finished in 'z' days more, then the number of men originally are
a(Z + z) / z

Here, a = 8, Z = 50, z = 10
Using these values in the shortcut, we get:
=
8(50 + 10) / 10
=
8 x 60 / 10
= 48
Hence, there are 48 boys.

34. A is thrice as fast as B and is therefore able to finish a work in 64 days less than B. Find the time in which they can do it working together.
  A.  24 days
  B.  20 days
  C.  22 days
  D.  26 days
     
   
View Answer

Shortcut:
If A is 'n' times as fast (or slow) as B, and is therefore able to finish a work in 'Z' days less (or more) than B, then the time in which they can do it working together is given by
Zn / (n2 − 1)

Here, n = 3, Z = 64
Using these values in the shortcut, we get:
=
64 x 3 / (32 − 1)
=
64 x 3 / 9 − 1
=
64 x 3 / 8
= 8 x 3 = 24
Hence, they will take 24 days.

35. Raj can finish a work in 15 days at 8 hrs/day. Sanju can finish it in 6
2 / 3
days at 9 hrs a day. Find in how many days they can finish it working together 10 hrs a day.
  A.  3 days
  B.  5 days
  C.  4 days
  D.  6 days
     
   
View Answer

Shortcut:
If a man can finish a work in d1 days at h1 hours a day and another man can finish the same work in d2 days at h2 hours a day, then the number of days in which they can finish the work, working together 'h' hours a day is
[
h1d1 x h2d2 / h1d1 + h2d2
]
1 / h
days
Here, h1 = 15, d1 = 8, h2 = 20/3, d2 = 9, h = 10
Using these values in the shortcut, we get:
=
[
15 x 8 x 20/3 x 9 / 15 x 8 + 20/3 x 9
]
1 / 10

=
[
15 x 8 x 60 / 120 + 60
]
1 / 10

=
[
15 x 8 x 60 / 180
]
1 / 10
= 4
Hence, they will take 4 days.

36. X can do a work in 6 days. Y takes 8 days to complete it. Z takes as long as X and Y would take working together. How long will it take Y and Z, X and Z, and X, Y and Z to complete the work together?
  A.  Y+Z: 1
2 / 5
days; X+Z: 2
3 / 11
days; X+Y+Z: 1
5 / 7
days
  B.  Y+Z: 2
2 / 5
days; X+Z: 2
2 / 11
days; X+Y+Z: 1
5 / 7
days
  C.  Y+Z: 2
2 / 5
days; X+Z: 1
2 / 11
days; X+Y+Z: 2
5 / 7
days
  D.  Y+Z: 1
2 / 5
days; X+Z: 2
2 / 11
days; X+Y+Z: 2
5 / 7
days
     
   
View Answer

Shortcut:
If X can do a work in 'a' days, Y takes 'b' days to complete it and Z takes as long as X and Y would take working together, the Y and Z together take to complete the work =
ab / 2a + b
days
X and Z together take to complete the work in
ab / a + 2b
days
X, Y and Z together take to complete the work in
ab / 2(a + b)
days
Here, a = 6, b = 8
Using these values in the shortcut, we get:
Y + Z together take to complete the work in
6 x 8 / 2 x 6 + 8
=
6 x 8 / 12 + 8
=
6 x 8 / 20
=
12 / 5
= 2
2 / 5

Hence, Y+Z will take 2
2 / 5
days
X + Z together take to complete the work in
6 x 8 / 6 + 2 x 8
=
6 x 8 / 6 + 16
=
48 / 22
=
24 / 11
= 2
2 / 11

Hence, X + Z will take 2
2 / 11
days
X +Y + Z together take to complete the work in
6 x 8 / 2(6 + 8)
=
6 x 8 / 2 x 14
=
3 x 4 / 7
=
12 / 7
= 1
5 / 7

Hence, X + Y + Z will take 1
5 / 7
days

37. Amit is twice as good a workman as Bhanu. Together, they finish the work in 14 days. In how many days can it be done by each separately?
  A.  Amit: 20 days; Bhanu: 40 days
  B.  Amit: 22 days; Bhanu: 44 days
  C.  Amit: 23 days; Bhanu: 46 days
  D.  Amit: 21 days; Bhanu: 42 days
     
   
View Answer

Shortcut:
X is n times as good a workman as Y. If together, they finish the work in 'm' days, then X and Y separately can do the same work in
(
n + 1 / n
)
m days and (n + 1)m days respectively.
Here, n = 2, m = 14
Using these values in the shortcut, we get:
Amit =
(
2 + 1 / 2
)
14 =
(
3 / 2
)
14 = 3 x 7 = 21
Hence, Amit will do in 21 days.
Bhanu = (n + 1)m = (2 + 1)14 = 3 x 14 = 42
Hence, Bhanu will finish it in 42 days.

38. Amit and Bhim together can do a piece of work in 3 days. If Amit does thrice as much work as Bhim in a given time, find how long Amit alone would take to do the work?
  A.  3 days
  B.  5 days
  C.  4 days
  D.  6 days
     
   
View Answer

Shortcut:
X is n times as good a workman as Y. If together, they finish the work in 'm' days, then X and Y separately can do the same work in
(
n + 1 / n
)
m days and (n + 1)m days respectively.
Here, n = 3, m = 3
Using these values in the shortcut, we get:
Amit =
3 + 1 / 3
x 3 = 4
Hence, Amit will do in 4 days.

39. 5 women and 2 girls working together can do 4 times as much work per hour as a woman and girl together. Compare the work of a woman with that of a girl.
  A.  Woman:Girl = 2 : 1; i.e woman is twice as efficient as a girl
  B.  Woman:Girl = 3 : 1; i.e woman is thrice as efficient as a girl
  C.  Woman:Girl = 1 : 1; i.e woman is same as efficient as a girl
  D.  Woman:Girl = 4:1; i.e woman is four times as efficient as a girl
     
   
View Answer

Shortcut:
If m1 men and b1 boys working together can do n times as much work per hour as m2 men and b2 boys together, then the comparison of the work of a man with that of a boy is given by
Man / Boy
=
nb2 − b1 / m1 − nm2

Here, m1 = 5, n = 4, b1 = 2, m2 = 1, b2 = 1
Using these values in the shortcut, we get:
Woman / Girl
=
(4 x 1) − 2 / (5 − 4) x 1
=
2 / 1

Hence, a woman is twice as efficient as a girl.

40. Ajay and Brij can do a work in 45 and 40 days respectively. They began the work together, but Ajay left after some time and Brij finished the remaining work in 23 days. After how many days did Ajay leave?
  A.  7 days
  B.  9 days
  C.  11 days
  D.  13 days
     
   
View Answer

Shortcut:
X and Y can do a work in 'a' and 'b' days respectively, they began the work together, but X left after some time and Y finished the remaining work in 'c' days, then the number of days after which X left is given by
(
ab / a + b
)(
b − c / b
)

Here, a = 45, b = 40, c = 23
Using these values in the shortcut, we get:
(
45 x 40 / 45 + 40
)(
40 − 23 / 40
)
=
(
45 x 40 / 85
)(
17 / 40
)
= 9
Hence, Ajay left after 9 days.

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