Time and Work

Question: A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :
[A].

4 days

[B].

6 days

[C].

8 days

[D].

18 days

Answer: Option A

Explanation:

Ratio of rates of working of A and B = 2 : 1.

So, ratio of times taken = 1 : 2.

B’s 1 day’s work =	1	.
	12

A’s 1 day’s work =	1	; (2 times of B’s work)
	6

(A + B)’s 1 day’s work =		1	+	1		=	3	=	1	.
		6		12			12		4

So, A and B together can finish the work in 4 days.

Question: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
[A].

8 hours

[B].

10 hours

[C].

12 hours

[D].

24 hours

Answer: Option C

Explanation:

A’s 1 hour’s work =	1	;
	4

(B + C)’s 1 hour’s work =	1	;
	3

(A + C)’s 1 hour’s work =	1	.
	2

(A + B + C)’s 1 hour’s work =		1	+	1		=	7	.
		4		3			12

B’s 1 hour’s work =		7	–	1		=	1	.
		12		2			12

B alone will take 12 hours to do the work.

Question: A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :
[A].

4 days

[B].

6 days

[C].

8 days

[D].

12 days

Answer: Option C

Explanation:

(A + B + C)’s 1 day’s work =	1	;
	6

(A + B)’s 1 day’s work =	1	;
	8

(B + C)’s 1 day’s work =	1	.
	12

(A + C)’s 1 day’s work	= 2 x 1 – 1 + 1 6 8 12
	= 1 – 5 3 24
	= 3 24
	= 1 . 8

So, A and C together will do the work in 8 days.

Question: Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
[A].

7 hours 30 minutes

[B].

8 hours

[C].

8 hours 15 minutes

[D].

8 hours 25 minutes

Answer: Option C

Explanation:

Number of pages typed by Ravi in 1 hour =	32	=	16	.
	6		3

Number of pages typed by Kumar in 1 hour =	40	= 8.
	5

Number of pages typed by both in 1 hour =		16	+ 8		=	40	.
		3				3

Time taken by both to type 110 pages =		110 x	3		hours
			40

= 8	1	hours (or) 8 hours 15 minutes.
	4

Question: A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
[A].

9	1	days
	5

[B].

9	2	days
	5

[C].

9	3	days
	5

[D].

10

Answer: Option C

Explanation:

(A + B + C)’s 1 day’s work =	1	,
	4

A’s 1 day’s work =	1	,
	16

B’s 1 day’s work =	1	.
	12

C’s 1 day’s work =	1	–		1	+	1		=		1	–	7		=	5	.
	4			16		12				4		48			48

So, C alone can do the work in	48	= 9	3	days.
	5		5

Question:
If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:

[A].

4 days

[B].

5 days

[C].

6 days

[D].

7 days

Answer: Option A

Explanation:

Let 1 man’s 1 day’s work = x and 1 boy’s 1 day’s work = y.

Then, 6x + 8y =	1	and 26x + 48y =	1	.
	10		2

Solving these two equations, we get : x =	1	and y =	1	.
	100		200

(15 men + 20 boy)’s 1 day’s work =		15	+	20		=	1	.
		100		200			4

15 men and 20 boys can do the work in 4 days.

Question:
4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

[A].

35

[B].

40

[C].

45

[D].

50

Answer: Option B

Explanation:

Let 1 man’s 1 day’s work = x and 1 woman’s 1 day’s work = y.

Then, 4x + 6y =	1	and 3x + 7y =	1	.
	8		10

Solving the two equations, we get: x =	11	, y =	1
	400		400

1 woman’s 1 day’s work =	1	.
	400

10 women’s 1 day’s work =		1	x 10		=	1	.
		400				40

Hence, 10 women will complete the work in 40 days.

Question:
10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

[A].

3

[B].

5

[C].

7

[D].

Cannot be determined

Answer: Option C

Explanation:

1 woman’s 1 day’s work =	1
	70

1 child’s 1 day’s work =	1
	140

(5 women + 10 children)’s day’s work =		5	+	10		=		1	+	1		=	1
		70		140				14		14			7

5 women and 10 children will complete the work in 7 days.

Question: Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?
[A].

3 : 4

[B].

4 : 3

[C].

5 : 3

[D].

Data inadequate

Answer: Option B

Explanation:

(20 x 16) women can complete the work in 1 day.

1 woman’s 1 day’s work =	1	.
	320

(16 x 15) men can complete the work in 1 day.

1 man’s 1 day’s work =	1
	240

So, required ratio	= 1 : 1 240 320
	= 1 : 1 3 4
	= 4 : 3 (cross multiplied)

Question:
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

[A].

12 days

[B].

15 days

[C].

16 days

[D].

18 days

Answer: Option B

Explanation:

A’s 2 day’s work =		1	x 2		=	1	.
		20				10

(A + B + C)’s 1 day’s work =		1	+	1	+	1		=	6	=	1	.
		20		30		60			60		10

Work done in 3 days =		1	+	1		=	1	.
		10		10			5

Now,	1	work is done in 3 days.
	5

Whole work will be done in (3 x 5) = 15 days.