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11. Wages for 45 womnen amount to Rs 31050 in 48 days. How many men must work 16 days to receive Rs 11500, the daily wages of a man being double those of a woman?
  A.  30 men
  B.  25 men
  C.  20 men
  D.  18 men
     
   
View Answer

Shortcut:
Wages for 'a' women amount to Rs Z1 in d1 days. If the daily wage of a man is n times that of a woman, then the number of men that receive Rs Z2, for the work of d2 days is
(
Z2 / Z1
)
x
(
d1 / d2
)
x
(
a / n
)

Here, a = 45, Z1 = 31050, d1 = 48, n = 2, Z2 = 11500, d2 = 16
Putting these values in the shortcut, we get:
Required Men =
(
11500 / 31050
)
x
(
48 / 16
)
x
(
45 / 2
)

=
(
1150 / 3105
)
x 3 x
(
45 / 2
)

=
1150 x 3 x 45 / 3105 x 2
=
575 / 23
= 25
Hence, the required number of men is 25.

12. Wages of 20 boys for 15 days is Rs 4500. If the daily wage of a man is one and half times that of a boys, how many men must work for 30 days to earn Rs 6750?
  A.  10 men
  B.  12 men
  C.  20 men
  D.  16 men
     
   
View Answer

Shortcut:
Wages for 'a' women amount to Rs Z1 in d1 days. If the daily wage of a man is n times that of a woman, then the number of men that receive Rs Z2, for the work of d2 days is
(
Z2 / Z1
)
x
(
d1 / d2
)
x
(
a / n
)

Here, a = 20, Z1 = 4500, d1 = 15, n = 1
1 / 2
or
3 / 2
, Z2 = 6750, d2 = 30
Putting these values in the shortcut, we get:
Required Men =
(
6750 / 4500
)
x
(
15 / 30
)
x
(
20 / 3/2
)

=
(
675 / 450
)
x
(
1 / 2
)
x
40 / 3

=
675 x 20 / 450 x 3
=
675 x 2 / 45 x 3
= 5 x 2 = 10
Hence, the required number of men is 10.

13. 3 men and 4 boys can earn Rs 756 in 7 days. 11 menand 13 boys can earn Rs 3008 in 8 days. In what time will 7 men with 9 boys earn Rs 1240
  A.  4 days
  B.  7 days
  C.  2 days
  D.  5 days
     
   
View Answer

Shortcut:
a1 men and b1 boys can earn Rs Z1 in d1 days, if a2 men and b2 boys can earn Rs Z2 in d2 days, then the following relationship is obtained
men / boys
=
[
Z1b2d2 − Z2b1d1 / Z2a1d1 − Z1a2d2
]

Here, a1 = 3, b1 = 4, Z1 = 756, d1 = 7, a2 = 11, b2 = 13, Z2 = 3008, d2 = 8
Putting these values in the shortcut, we get:
men / boys
=
[
756 x 13 x 8 − 3008 x 4 x 7 / 3008 x 3 x 7 − 756 x 11 x 8
]

=
(
78624 − 84224 / 63168 − 66528
)

=
(
−5600 / −3360
)
=
5 / 3

Now, 3m + 4b earn in 1 day = Rs
756 / 7
= Rs 108
or, 3m x 4 x
3 / 5
m earn in 1 day Rs 108
or
27 / 5
m earn in 1 day Rs 108
∴ 1m in 1 day earns Rs
108 x 5 / 27
= Rs 20
Thus, we get that a man earns Rs 20 daily and a boy earns Rs 20 x
3 / 5
= Rs 12 daily
Since, 7m + 9b earn Rs(7 x 20 + 9 x 12) = Rs 248 in 1 day.
∴ 7m + 9b earn Rs 1240 in 5 days.

14. If 5 men with 7 boys can earn Rs 3825 in 6 days and 2 men with 3 boys can earn Rs 1050 in 4 days, in what time will 7 men with 6 boys earn Rs 15000?
  A.  12 days
  B.  15 days
  C.  20 days
  D.  22 days
     
   
View Answer

Shortcut:
a1 men and b1 boys can earn Rs Z1 in d1 days, if a2 men and b2 boys can earn Rs Z2 in d2 days, then the following relationship is obtained
men / boys
=
[
Z1b2d2 − Z2b1d1 / Z2a1d1 − Z1a2d2
]

Here, a1 = 5, b1 = 7, Z1 = 3825, d1 = 6, a2 = 2, b2 = 3, Z2 = 1050, d2 = 4
Putting these values in the shortcut, we get:
men / boys
=
[
3825 x 3 x 4 − 1050 x 7 x 6 / 1050 x 5 x 6 − 3825 x 2 x 4
]

=
(
45900 − 44100 / 31500 − 30600
)

=
(
1800 / 900
)
=
2 / 1

Men : Boys = 2 : 1
i.e. 1 man = 2 boys
Now, (5m + 7b) earn in 6 days Rs 3825.
(5m + 7b) can earn in 1 day Rs
3825 / 6
= Rs 637.5
5m +
7 / 2
m can earn in 1 day Rs 637.5
or,
17 / 2
m can earn in 1 day Rs 637.5
∴ 1m can earn in 1 day
637.5 x 2 / 17
= Rs 75
and 1b can earn in 1 day Rs
75 / 2

(7m + 6b) can earn in 1 day = 7 x 75 + 6 x
75 / 2
= Rs 750
∴ Rs 15000 can be earned by (7m + 6b) in
15000 / 750
= 20 days.

15. A, B and C together earn Rs 1080 in 9 days. A and C together earn Rs 360 in 5 days. B and C together earn Rs 640 in 10 days. Find the daily earning of C.
  A.  Rs 21
  B.  Rs 16
  C.  Rs 27
  D.  Rs 25
     
   
View Answer

Shortcut:
If X, Y and Z together earn Rs a1 in d1 days, X and Z together earn Rs a1 in d2 days and Y and Z together earn Rs a3 in d3 days, then
The daily earning of A =
a1d3 − a3d1 / d1d3

The daily earning of B =
a1d2 − a2d1 / d1d2

The daily earning of C =
[
a3 / d3
+
a2 / d2
−
a1 / d1
]

Here, a1 = 1080, d1 = 9, a2= 360, d2 = 5, a3 = 640, d3 = 10
Using these values in the shortcut, we get:
Daily earning of C =
[
640 / 10
+
360 / 5
−
1080 / 9
]
= 64 + 72 − 120 = 16
Hence, the daily earning of C is Rs 16.

16. A,B and C together earn Rs 2160 in 18 days. A and C together earn Rs 930 in 10 days. B and C together earn Rs 1540 in 20 days. Find the daily earning of C.
  A.  Rs 45
  B.  Rs 55
  C.  Rs 50
  D.  Rs 60
     
   
View Answer

Shortcut:
If X, Y and Z together earn Rs a1 in d1 days, X and Z together earn Rs a1 in d2 days and Y and Z together earn Rs a3 in d3 days, then
The daily earning of A =
a1d3 − a3d1 / d1d3

The daily earning of B =
a1d2 − a2d1 / d1d2

The daily earning of C =
[
a3 / d3
+
a2 / d2
−
a1 / d1
]

Here, a1 = 2160, d1 = 18, a2= 930, d2 = 10, a3 = 1540, d3 = 20
Using these values in the shortcut, we get:
Daily earning of C =
[
1540 / 20
+
930 / 10
−
2160 / 18
]
= 77 + 93 − 120 = 50
Hence, the daily earning of C is Rs 50.

17. Wages of 10 women for 5 days is Rs 625. The daily wage of a man is twice that of a woman. How many men must work for 8 days to earn Rs 800?
  A.  5 men
  B.  3 men
  C.  6 men
  D.  4 men
     
   
View Answer

Shortcut:
Wages for 'a' women amount to Rs Z1 in d1 days. If the daily wage of a man is n times that of a woman, then the number of men that receive Rs Z2, for the work of d2 days is
(
Z2 / Z1
)
x
(
d1 / d2
)
x
(
a / n
)

Here, a = 10, Z1 = 625, d1 = 5, n = 2, Z2 = 800, d2 = 8
Putting these values in the shortcut, we get:
Required Men =
(
800 / 625
)
x
(
5 / 8
)
x
(
10 / 2
)

=
(
160 / 125
)
x
(
5 / 8
)
x 5
=
20 x 5 x 5 / 125
= 4
Hence, the required number of men is 4.

18. Seema can do a work in 25 days. Seema and Meena together do the same work in 20 days. If they are paid Rs 250 for the work, how much money should Meena get?
  A.  Rs 40
  B.  Rs 50
  C.  Rs 60
  D.  Rs 55
     
   
View Answer

Shortcut:
X can do a work in 'a' days. With the help of another person Y, he can do the same work in 'b' days. If they get Rs M for that work, then the share of X and Y is given by Rs
Mb / a
and Rs
M(a − b) / a

Here, a = 25, b = 20, M = 250
Using these values in shortcut, we get:
Share of Meena =
250(25 − 20) / 25
=
250 x 5 / 25
= 10 x 5 = 50
Hence, the share of Meena is Rs 50.

19. A, B and C contract to do a work for Rs 3250. A can do the work in 10 days, B in 15 days and C in 20 days. If they work together to do the work, what is the share of B?
  A.  Rs 1000
  B.  Rs 1300
  C.  Rs 1120
  D.  Rs 900
     
   
View Answer

Shortcut:
X, Y and Z can do a work in a, b and c days respectively. If they work together they get an amount of Rs Z, then
the share of X = Rs
Zbc / ab + ac + bc

Share of Y = Rs
Zac / ab + ac + bc

Share of Z = Rs
Zab / ab + ac + bc
and ratio of their shares is X : Y : Z = bc : ac : ab
Here, a = 10, b = 15, c = 20, Z = 3250
Using these values in shortcut, we get:
Share of B = Rs
3250 x 10 x 20 / 10 x 15 + 10 x 20 + 15 x 20

= Rs
3250 x 10 x 20 / 150 + 200 + 300

= Rs
3250 x 10 x 20 / 650

= Rs
3250 x 4 / 13
= 250 x 4 = 1000
Hence, the share of B is Rs 1000.

20. A, B and C together earn Rs 375 in 5 days. A and C together earn Rs 400 in 4 days. B and C together earn Rs 450 in 9 days. Find the daily earning of A.
  A.  Rs 52
  B.  Rs 60
  C.  Rs 25
  D.  Rs 45
     
   
View Answer

Shortcut:
If X, Y and Z together earn Rs a1 in d1 days, X and Z together earn Rs a1 in d2 days and Y and Z together earn Rs a3 in d3 days, then
The daily earning of A =
a1d3 − a3d1 / d1d3

The daily earning of B =
a1d2 − a2d1 / d1d2

The daily earning of C =
[
a3 / d3
+
a2 / d2
−
a1 / d1
]

Here, a1 = 375, d1 = 5, a2= 400, d2 = 4, a3 = 450, d3 = 9
Using these values in the shortcut, we get:
Daily earning of A =
375 x 9 − 450 x 5 / 5 x 9

=
3375 − 2250 / 45
=
1125 / 45
= 25
Hence, the daily earning of A is Rs 25.

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