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11. Ajay can do a piece of work in 30 days while Babbi can do it in 40 days. Ajay and Babbi working together can do it in:
  A.  17
1 / 7
days
  B.  19
1 / 7
days
  C.  17
2 / 7
days
  D.  19
2 / 7
days
     
   
View Answer

Shortcut: If A can do a piece of work in x days and B can do it in y days then A and B all together will do work in
xy / x + y
days
x = 30, y = 40
Using these values in shortcut, we get:
30 x 40 / 30 + 40
=
30 x 40 / 70
=
30 x 4 / 7
=
120 / 7
= 17
1 / 7

Hence, they will take 17
1 / 7
days.

12. A can do
1 / 3
of a work in 5 days and B can do
2 / 5
of the work in 10 days. In how many days both A and B together can do the work?
  A.  7
3 / 8
days
  B.  9
3 / 8
days
  C.  6
3 / 8
days
  D.  8
3 / 8
days
     
   
View Answer

Shortcut:
If A can do a piece of work in x days and B can do it in y days then A and B all together will do work in
xy / x + y
days
A can do the whole work in 5 x 3 = 15 days
B can do the whole work in
10 x 5 / 2
= 25 days
Here, x = 15, y = 25
Using these values in shortcut, we get:
15 x 25 / 15 + 25
=
15 x 25 / 40
=
3 x 25 / 8
=
75 / 8
= 9
3 / 8

Hence, they will take 9
3 / 8
days.

13. A can do a piece of work in 2 days, and B can do it in 4 days. If C, who can do the work in 6 days, joins them, how long will they take to complete the work?
  A.  1
2 / 11
days
  B.  1
1 / 11
days
  C.  2
1 / 11
days
  D.  2
3 / 11
days
     
   
View Answer

Shortcut:
If P, Q and R can do a work in x, y and z days respectively then all of them working together can finish the work in
xyz / xy + yz + zx
days
Here, x = 2, y = 4, z = 6
Using these values in shortcut, we get:
=
2 x 4 x 6 / 2 x 4 + 4 x 6 + 6 x 2
=
2 x 4 x 6 / 8 + 24 + 12
=
2 x 4 x 6 / 44
=
12 / 11
= 1
1 / 11

Hence, they will take 1
1 / 11
days.

14. A, B, and C can do a piece of work in 6, 12 and 24 days respectively. They altogether will complete the work in:
  A.  3
3 / 7
days
  B.  2
3 / 7
days
  C.  4
3 / 7
days
  D.  6
3 / 7
days
     
   
View Answer

Shortcut:
If P, Q and R can do a work in x, y and z days respectively then all of them working together can finish the work in
xyz / xy + yz + zx
days
Here, x = 6, y = 12, z = 24
Using these values in shortcut, we get:
=
6 x 12 x 24 / 6 x 12 + 12 x 24 + 24 x 6
=
6 x 12 x 24 / 72 + 288 + 144
=
6 x 12 x 24 / 504
=
24 / 7
= 3
3 / 7

Hence, they will take 3
3 / 7
days.

15. A and B together can do a piece of work in 3 days and A alone can do it in 6 days. In how many days can B alone do it?
  A.  4 days
  B.  6 days
  C.  5 days
  D.  7 days
     
   
View Answer

Shortcut:
If P and Q together can do a piece of work in x days and P alone can do it in y days, then Q alone can do the work in
xy / y − x
days
Here, x = 3, y = 6
Using these values in shortcut, we get:
=
3 x 6 / 6 − 3
=
3 x 6 / 3
= 6
Hence, B will take 6 days.

16. A and B can together do a piece of work in 15 days. B alone can do it in 20 days. A alone can do it in:
  A.  60 days
  B.  55 days
  C.  65 days
  D.  70 days
     
   
View Answer

Shortcut:
If P and Q together can do a piece of work in x days and P alone can do it in y days, then Q alone can do the work in
xy / y − x
days
Here, x = 15, y = 20
Using values in shortcut, we get:
=
15 x 20 / 20 − 15
=
15 x 20 / 5
= 3 x 20 = 60
Hence, A will take 60 days.

17. A, B and C can finish a job in 8 days while A and B finish it in 12 days, C alone will finish the job in:
  A.  20 days
  B.  22 days
  C.  26 days
  D.  24 days
     
   
View Answer

Shortcut:
If P and Q together can do a piece of work in x days and P alone can do it in y days, then Q alone can do the work in
xy / y − x
days
Here, x = 8, y = 12
Using values in shortcut, we get:
=
8 x 12 / 12 − 8
=
8 x 12 / 4
= 2 x 12 = 24
Hence, C will take 24 days.

18. B takes three times to do a work as long a A and C together and C takes twice as long as A and B together. The three men together complete the work in 10 days. How long would each take separately?
  A.  Days taken by A: 20 days; Days taken by B: 42 days; Days taken by C: 32 days
  B.  Days taken by A: 28 days; Days taken by B: 38 days; Days taken by C: 28 days
  C.  Days taken by A: 24 days; Days taken by B: 40 days; Days taken by C: 30 days
  D.  Days taken by A: 18 days; Days taken by B: 42 days; Days taken by C: 34 days
     
   
View Answer

Shortcut:
To do certain work Q would take n times as long as P and R together and R m times as long as P and Q together. If the three men together complete the work in x days, then if the number of days taken by Q will be Number of days taken by (P + Q + R) x (n + 1) and the number of days taken by R will be = Number of days taken by (P + Q + R) x (m + 1)

Number of days taken by B = Number of days taken by A + B + C x (3 + 1) 10(3+1) = 40 days

Similarly,
Number of days taken by C = Number of days taken by A + B + C x (2 + 1) 10(2 + 1) = 30 days

∴ Number of days taken by A =
1 / 1/10 − (1/40 + 1/30)

=
1 / 1/10 − (3 + 4)/120

=
1 / 1/10 − 7/120

=
1 / (12 − 7)/120

=
1 / 5/120
=
120 / 5
= 24
Hence, A will take 24 days.
B will take 40 days.
C will take 30 days.

19. If 3 men or 4 women can reap a field in 43 days, how long will 7 men and 5 women take to reap it?
  A.  10 days
  B.  12 days
  C.  14 days
  D.  16 days
     
   
View Answer

Shortcut:
If a1 men or b1 women can reap a field in 'Z' days, then a2 men and b2 women will reap the field in =
Z(a1b1) / a2b1 + a1b2
days
Here, a1 = 3, b1 = 4, Z = 43, a2 = 7, b2 = 5
Using these values in the shortcut, we get:
=
43(3 x 4) / 7 x 4 + 3 x 5
=
43 x 12 / 28 + 15
=
43 x 12 / 43
= 12
Hence, they will reap the field in 12 days.

20. If 4 men or 6 boys can finish a piece of work in 20 days, in how many days can 6 men and 11 boys finish it?
  A.  6 days
  B.  4 days
  C.  5 days
  D.  8 days
     
   
View Answer

Shortcut:
If a1 men or b1 women can reap a field in 'Z' days, then a2 men and b2 women will reap the field in =
Z(a1b1) / a2b1 + a1b2
days
Here, a1 = 4, b1 = 6, Z = 20, a2 = 6, b2 = 11
Using these values in the shortcut, we get:
=
20(4 x 6) / 6 x 6 + 4 x 11
=
20 x 24 / 36 + 44
=
20 x 24 / 80
= 6
Hence, they will reap the field in 6 days.

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