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1. A can do a work in 6 days and B can do the same work in 5 days. The contract for the work is Rs 220. How much shall B get if both of them work together?
  A.  Rs 120
  B.  Rs 150
  C.  Rs 80
  D.  Rs 100
     
   
View Answer

Shortcut:
X can do a work in a days and Y can do the same work in b days. If the contract for the work is Rs Z, and both of them work together, then the share of X and Y is given by
Z / a + b
x b and
Z / a + b
x a respectively.
Here, a = 6, b = 5, Z = 220
Using these values in the shortcut, we get:
X share =
220 / 6 + 5
x 5 =
220 / 11
x 5 = 20 x 5 = 100
Hence, share of A is Rs 100
Y share =
220 / 6 + 5
x 6 =
220 / 11
x 6 = 20 x 6 = 120
Hence, share of B is Rs 120.

2. Umesh can do a certain work in 15 days while Sachin can do it in 25 days. Both work together and finish the work. In what ratio should the total earnings be divided between them?
  A.  2 : 5
  B.  3 : 5
  C.  5 : 3
  D.  5 : 2
     
   
View Answer

Shortcut:
X can do a work in a days and Y can do the same work in b days. If the contract for the work is Rs Z, and both of them work together, then the ratio of share of X and Y is given by
Z / a + b
x b :
Z / a + b
x a
Umesh : Sachin =
Z / a + b
x b :
Z / a + b
x a
or y:x (i.e the ratio in which the wages are divided is in inverse proportion to the time taken by them to do the work alone) = 25:15 = 5:3

3. A, B and C can do a work in 4, 6 and 10 days respectively. They finish the work together and earn Rs 310. What is the share of each?
  A.  A's share:Rs 130; B's share:Rs 120; C's share:Rs 60
  B.  A's share:Rs 150; B's share:Rs 100; C's share:Rs 60
  C.  A's share:Rs 100; B's share:Rs 150; C's share:Rs 60
  D.  A's share:Rs 60; B's share:Rs 150; C's share:Rs 100
     
   
View Answer

A's share: B's share: C's share =
1 / 4
:
1 / 6
:
1 / 10
= 15 : 10 : 6
A's share =
15 / 15 + 10 + 6
x 310 = Rs 150
B's share =
10 / 15 + 10 + 6
x 310 = Rs 100
C's share =
6 / 15 + 10 + 6
x 310 = Rs 60

4. A, B and C can do a work in 6, 8 and 12 days respectively. Doing that work together they get an amount of Rs 1350. What is the share of B in that amount?
  A.  Rs 450
  B.  Rs 400
  C.  Rs 450
  D.  Rs 550
     
   
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 = 6, b = 8, c = 12, Z = 1350
Using these values in shortcut, we get:
Share of B = Rs
1350 x 6 x 12 / 6 x 8 + 6 x 12 + 8 x 12

= Rs
1350 x 6 x 12 / 48 + 72 + 96

= Rs
1350 x 6 x 12 / 216

= Rs
1350 / 3
= Rs 450
Hence, the share of B is Rs 450.

5. A, B and C contract to do a work for Rs 4200. A can do the work in 6 days, B in 10 days and C in 12 days. If they work together to do the work, what is the share of C?
  A.  Rs 1100
  B.  Rs 800
  C.  Rs 1500
  D.  Rs 1000
     
   
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 M, then
the share of X = Rs
Mbc / ab + ac + bc

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

Share of Z = Rs
Mab / ab + ac + bc
and ratio of their shares is X : Y : Z = bc : ac : ab
Here, a = 6, b = 10, c = 12, M = 4200
Using these values in shortcut, we get:
Share of C = Rs
4200 x 6 x 10 / 6 x 10 + 6 x 12 + 10 x 12

= Rs
4200 x 6 x 10 / 60 + 72 + 120

= Rs
4200 x 6 x 10 / 252

= Rs
4200 x 10 / 42
= 100 x 10 = 1000
Hence, the share of C is Rs 1000.

6. A man can do a work in 10 days. With the help of a boy he can do the same work in 6 days. If they get Rs 50 for that work, what is the share of that boy?
  A.  Rs 25
  B.  Rs 20
  C.  Rs 10
  D.  Rs 15
     
   
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 = 10, b = 6, M = 50
Using these values in shortcut, we get:
Share of man = Rs
50 x 6 / 10
= 5 x 6 = 30
Hence, the share of man is Rs 50.
Share of boy =
50(10 − 6) / 10
=
50 x 4 / 10
= 5 x 4 = 20
Hence, the share of boy is Rs 20.

7. Hemu can do a work in 20 days. Hemu and Prashant together do the same work in 15 days. If they are paid Rs 400 for that work, what is the share of each?
  A.  Rs 240; Rs 160
  B.  Rs 220; Rs 180
  C.  Rs 300; Rs 100
  D.  Rs 150; Rs 250
     
   
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 = 20, b = 15, M = 400
Using these values in shortcut, we get:
Share of Hemu = Rs
400 x 15 / 20
= 20 x 15 = 300
Hence, the share of Hemu is Rs 300.
Share of Prashant =
400(20 − 15) / 20
= 20 x 5 = 100
Hence, the share of Prashant is Rs 100.

8. A and B undertake to do a work for Rs 56. A can do it alone in 7 days and B in 8 days. If with the assistance of a boy they finish the work in 3 days, then how much amount the boy will get?
  A.  Rs 11
  B.  Rs 12
  C.  Rs 15
  D.  Rs 10
     
   
View Answer

Shortcut:
X and Y undertake to do a work for Rs M. X can do it alone in 'a' days and Y in 'b' days. If with the assistance of a boy they finish the work in 'q' days, then the share of X is Rs
qM / a
, share of Y is Rs
qM / b
and the share of boy is M
[
1 −
(
a + b / ab
)
q
]
and the ratio of their share X : Y : Boy = qb : qa : ab
Here, a = 7, b = 8, q = 3, M = 56
Using these values in shortcut, we get:
Share of boy = 56
[
1 −
(
7 + 8 / 7 x 8
)
3
]

= 56
[
1 −
(
15 / 56
)
3
]

= 56
[
1 −
(
45 / 56
)]

= 56
(
56 − 45 / 56
)
= 56
(
11 / 56
)
= 11
Hence, the share of boy is Rs 11.

9. A and B undertake to do a work together for Rs 300. If A alone can do it in 8 days and B alone in 12 days. But with the help of C they finish it in 4 days. Find the share of C.
  A.  Rs 55
  B.  Rs 50
  C.  Rs 60
  D.  Rs 40
     
   
View Answer

Shortcut:
X and Y undertake to do a work for Rs M. X can do it alone in 'a' days and Y in 'b' days. If with the assistance of a boy they finish the work in 'q' days, then the share of X is Rs
qM / a
, share of Y is Rs
qM / b
and the share of boy is M
[
1 −
(
a + b / ab
)
q
]
and the ratio of their share X:Y:Boy = qb:qa:ab
Here, a = 8, b = 12, q = 4, M = 300
Using these values in shortcut, we get:
Share of C = 300
[
1 −
(
8 + 12 / 8 x 12
)
4
]

= 300
[
1 −
(
20 / 96
)
4
]

= 300
[
1 −
(
20 x 4 / 96
)
]

= 300
[
1 −
(
80 / 96
)
]

= 300
(
96 − 80 / 96
)

= 300
(
16 / 96
)
= 50
Hence, the share of C is Rs 50.

10. A, B and C contract a work for Rs 550. Together A and B are supposed to
7 / 11
of the work. How much does C get?
  A.  Rs 250
  B.  Rs 150
  C.  Rs 200
  D.  Rs 300
     
   
View Answer

Shortcut:
X, Y and Z contract a work for Rs M. If together, X and Y are supposed to do
a / b
of the work, then the share of Z is Rs M
(
1 −
a / b
)

Here, M = 550, a= 7, b = 11
Putting these values in the shortcut, we get:
Share of C = 550
(
1 −
7 / 11
)
= 550
(
11 − 7 / 11
)
= 550
(
4 / 11
)
= 50 x 4 = 200
Hence, the share of C is Rs 200.

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