## Time and Work

#### Time and Work

1. A can finish a work in 7 days. B can finish the same work in 9 days. The number days required to finish the same work by both of them together is

1.  A’s 1 day’s work = 1 7

 B’s 1 day’s work = 1 9

∴ (A + B)’s 1 day’s work
 = 1 + 1 7 9

 = 1440 = 40 = 3 1 days 468 13 13

 ∴ Required time = 63 days 16

 = 3 15 days 16

##### Correct Option: C

 A’s 1 day’s work = 1 7

 B’s 1 day’s work = 1 9

∴ (A + B)’s 1 day’s work
 = 1 + 1 7 9

 = 1440 = 40 = 3 1 days 468 13 13

 ∴ Required time = 63 days 16

 = 3 15 days 16

1. A, B and C working separately can do a piece of work in 11 days, 20 days and 55 days respectively. In how many days, the work will be completed if A is assisted by B and C on alternate days ?

1. (A + B)’s 1 day’s work

 = 1 + 1 11 20

 = 20 + 11 = 31 220 220

(A + C)’s 1 day’s work
 = 1 + 1 11 55

 = 5 + 1 = 6 55 55

Work done in first two days
 = 31 + 6 220 55

 = 31 + 24 = 55 = 1 220 220 4

∴ Required time = 2 × 4 = 8 days

##### Correct Option: D

(A + B)’s 1 day’s work

 = 1 + 1 11 20

 = 20 + 11 = 31 220 220

(A + C)’s 1 day’s work
 = 1 + 1 11 55

 = 5 + 1 = 6 55 55

Work done in first two days
 = 31 + 6 220 55

 = 31 + 24 = 55 = 1 220 220 4

∴ Required time = 2 × 4 = 8 days

1. A can do a piece of work in 12 days and B in 24 days. If they work together, in how many days will they finish the work?

1. (A + B)’s 1 day’s work

 = 1 + 1 12 24

 = 2 + 1 = 3 = 1 24 24 8

∴ Required time = 8 days

##### Correct Option: D

(A + B)’s 1 day’s work

 = 1 + 1 12 24

 = 2 + 1 = 3 = 1 24 24 8

∴ Required time = 8 days

1. A and B together can finish a job in 24 days, while A, B and C together can finish the same job in 8 days. C alone will finish the job in

1.  (A + B)’s 1 day’s work = 1 24

 (A + B + C)’s 1 day’s work = 1 6

 ∴ C’s 1 day’s work = 1 - 1 8 24

 = 3 - 1 = 2 = 1 24 24 12

∴ Required time = 12 days

##### Correct Option: A

 (A + B)’s 1 day’s work = 1 24

 (A + B + C)’s 1 day’s work = 1 6

 ∴ C’s 1 day’s work = 1 - 1 8 24

 = 3 - 1 = 2 = 1 24 24 12

∴ Required time = 12 days

1. A and B together can do a piece of work in 6 days and A alone can do it in 9 days. The number of days B will take to do it alone is

1.  (A + B)’s 1 day’s work = 1 6

 A’s 1 day’s work = 1 9

 ∴ B’s 1 day’s work = 1 - 1 6 9

 = 3 - 2 = 1 18 18

∴ Required time = 18 days

##### Correct Option: A

 (A + B)’s 1 day’s work = 1 6

 A’s 1 day’s work = 1 9

 ∴ B’s 1 day’s work = 1 - 1 6 9

 = 3 - 2 = 1 18 18

∴ Required time = 18 days