# Time and Work

A can do a work in 6 days and B in 9 days. How many days will both take together to complete the work?

[A]5.4 days

[B]7.5 days

[C]3.6 days

[D]3 days

**3.6 days**

According to question. A can finish the whole work in 6 days.

∴ A’s one day’s work =

Similiarly, B’s one day’s work =

(A+B)’s one day’s work =

Therefore, (A+B) can finish the whole work in days i.e. 3.6 days.

Hence option [C] is the right answer.

A and B together can complete a work in 8 days and B and C together in 12 days. All of the three together can complete the work in 6days. In how much time will A and C together complete the work?

[A]20

[B]8

[C]12

[D]10

**8**

Let A and C complete the work in x days

(A+B)’s one day’s work=

(B+C)’s one day’s work=

(C+A)’s one day’s work=

Then (A+B+B+C+C+A)’s one day’s work =

2(A+B+C)’s one day’s work =

(A+B+C)’s 1 day’s work =

According to the question (A+B+C)’s 1 day’s work =

∴ x = = 8 days

∴ option [B] is the right answer.

A and B together can do a piece of work in 10 days. A alone can do it in 30 days. The time in which B alone can do it is :

[A]10

[B]12

[C]20

[D]15

**15**

(A+B)’s 1 day’s work =

A’s 1 day’s work =

∴ B’s 1 day’s work =

=

Hence, B, alone can complete the work in 15 days.

A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they wil complete the same work in :

[A]4 days

[B] days

[C] days

[D] days

** days**

A’s 1 day’s work =

B’s 1 day’s work =

C’s 1 day’s work =

(A+B+C)’s 1 day’s work =

∴ The work will be completed by them in i.e. days.

A and B together can complete a piece of work in 72 days, B and C together can complete it in 120 days, and A and C together in 90 days. In what time can A alone complete the work?

[A]150 days

[B]80 days

[C]100 days

[D]120 dyas

**120 days**

(A+B)’s 1 day’s work =

(B+C)’s 1 day’s work =

(C+A)’s 1 day’s work =

Adding all three, 2(A+B+C)’s 1 days work =

∴ (A+B+C)’s 1 day’s work =

Now, A’s 1 day’s work = (A+B+C)’s 1 day’s work – (B+C)’s 1 day’s work

∴ A alone can comlete the work in 120 days.

Hence option [D] is correct.

A alone can complete a work in 12 days. A and B together can complete it in 8 days. How long will B alone take to complete the work?

[A]20 days

[B]24 days

[C]16 days

[D]18 days

**24 days**

A’s one day’s work

(A + B)’s one day’s work

∴ B’s one day’s work =

∴ B alone can do the work in 24 days.

Hence option [B] is the right answer.

A can do a piece of work in 4 hours, B and C can do it in 3 hours. A and C can do it in 2 hours. How long will B alone take to do it?

[A]8 hours

[B]24 hours

[C]10 hours

[D]12 hours

**12 hours**

A’s one hour’s work

(B + C)’s one hour’s work

(A + C)’s one hour’s work

∴ C’s one hour’s work

B’s one hour’s work

Hence B alone can do the work in 12 hours, so option [D] is correct answer.

A and B can do a work in 12 days, B and C in 15 days and C and A in 20 days. If A, B and C work together, they will complete the work in :

[A] days

[B]5 days

[C]10 days

[D] days

**10 days**

According to question,

A and B can do a work in 12 days

∴ (A + B)’s one day’s work

Similarly, (B + C)’s one day’s work

and (C + A)’s one day’s work

On adding all three,

∴ 2 (A + B + C)’s one day’s work

and (A + B + C)’s one day’s work

∴ A, B and C together can complete the work in 10 days.

A and B can do a piece of work in 72 days. B and C can do it in 120 days, A and C can do it in 90 days. In how many days all the three together can do the work ?

[A]150 days

[B]60 days

[C]80 days

[D]100 days

**60 days**

According to question,

(A + B)’s one day’s work

(B + C)’s one day’s work

and (C + A)’s one day’s work

On adding all three,

2 (A + B + C)’s one day’s work

∴ (A + B + C)’s one day’s work

∴ A, B and C together can finish the whole work in 60 days.

Hence option [B] is the right answer.

A paricular job can be completed by a team of 10 men in 12 days. The same job can be completed by a team of 10 women in 6 days. How many days are needed to complete the job if the two teams work together?

[A]18 days

[B]9 days

[C]6 days

[D]4 days

**4 days**

According to the question,

10 men’s one day’s work

∴ 1 man one day’s work

Similarly,

1 woman one day’s work

∴ (1 man + 1 woman)’s one day’s work

∴ (10 man + 10 woman)’s one day’s work

Therefore, both the team can finish the whole work in 4 days.

Hence option [D] is the right answer.