Time and Work

Question: A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
[A].

23 days

[B].

37 days

[C].

37

[D].

40 days

Answer: Option C

Explanation:

Whole work is done by A in		20 x	5		= 25 days.
			4

Now,		1 –	4		i.e.,	1	work is done by A and B in 3 days.
			5			5

Whole work will be done by A and B in (3 x 5) = 15 days.

A’s 1 day’s work =	1	, (A + B)’s 1 day’s work =	1	.
	25		15

B’s 1 day’s work =		1	–	1		=	4	=	2	.
		15		25			150		75

So, B alone would do the work in	75	= 37	1	days.
	2		2

Question: X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?
[A].

13	1	days
	3

[B].

15 days

[C].

20 days

[D].

26 days

Answer: Option A

Explanation:

Work done by X in 8 days =		1	x 8		=	1	.
		40				5

Remaining work =		1 –	1		=	4	.
			5			5

Now,	4	work is done by Y in 16 days.
	5

Whole work will be done by Y in		16 x	5		= 20 days.
			4

X’s 1 day’s work =	1	, Y’s 1 day’s work =	1	.
	40		20

(X + Y)’s 1 day’s work =		1	+	1		=	3	.
		40		20			40

Hence, X and Y will together complete the work in		40		= 13	1	days.
		3			3

Question: A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work?
[A].

40

[B].

50

[C].

54

[D].

60

Answer: Option D

Explanation:

(A + B)’s 20 day’s work =		1	x 20		=	2	.
		30				3

Remaining work =		1 –	2		=	1	.
			3			3

Now,	1	work is done by A in 20 days.
	3

Therefore, the whole work will be done by A in (20 x 3) = 60 days.

Question: A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?
[A].

18 days

[B].

24 days

[C].

30 days

[D].

36 days

Answer: Option A

Explanation:

2(A + B + C)’s 1 day’s work =		1	+	1	+	1		=	15	=	1	.
		30		24		20			120		8

Therefore, (A + B + C)’s 1 day’s work =	1	=	1	.
	2 x 8		16

Work done by A, B, C in 10 days =	10	=	5	.
	16		8

Remaining work =		1 –	5		=	3	.
			8			8

A’s 1 day’s work =		1	–	1		=	1	.
		16		24			48

Now,	1	work is done by A in 1 day.
	48

So,	3	work will be done by A in		48 x	3		= 18 days.
	8				8

Question: A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?
[A].

11:30 A.M.

[B].

12 noon

[C].

12:30 P.M.

[D].

1:00 P.M.

Answer: Option D

Explanation:

(P + Q + R)’s 1 hour’s work =		1	+	1	+	1		=	37	.
		8		10		12			120

Work done by P, Q and R in 2 hours =		37	x 2		=	37	.
		120				60

Remaining work =		1 –	37		=	23	.
			60			60

(Q + R)’s 1 hour’s work =		1	+	1		=	11	.
		10		12			60

Now,	11	work is done by Q and R in 1 hour.
	60

So,	23	work will be done by Q and R in		60	x	23		=	23	hours 2 hours.
	60			11		60			11

So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.

Question: A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :
[A].

8 days

[B].

10 days

[C].

12 days

[D].

15 days

Answer: Option C

Explanation:

(A + B)’s 1 day’s work =		1	+	1		=	1	.
		15		10			6

Work done by A and B in 2 days =		1	x 2		=	1	.
		6				3

Remaining work =		1 –	1		=	2	.
			3			3

Now,	1	work is done by A in 1 day.
	15

	2	work will be done by a in		15 x	2		= 10 days.
	3				3

Hence, the total time taken = (10 + 2) = 12 days.

Question: A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
[A].

5

[B].

5	1
	2

[C].

6

[D].

8

Answer: Option C

Explanation:

B’s 10 day’s work =		1	x 10		=	2	.
		15				3

Remaining work =		1 –	2		=	1	.
			3			3

Now,	1	work is done by A in 1 day.
	18

	1	work is done by A in		18 x	1		= 6 days.
	3				3

Question: A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :
[A].

1

4

[B].

1

10

[C].

7

15

[D].

8

15

Answer: Option D

Explanation:

A’s 1 day’s work =	1	;
	15

B’s 1 day’s work =	1	;
	20

(A + B)’s 1 day’s work =		1	+	1		=	7	.
		15		20			60

(A + B)’s 4 day’s work =		7	x 4		=	7	.
		60				15

Therefore, Remaining work =		1 –	7		=	8	.
			15			15

Question: A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?
[A].

11 days

[B].

13 days

[C].

20	3	days
	17

[D].

None of these

Answer: Option B

Explanation:

Ratio of times taken by A and B = 100 : 130 = 10 : 13.

Suppose B takes x days to do the work.

Then, 10 : 13 :: 23 : x         x =		23 x 13		x =	299	.
		10			10

A’s 1 day’s work =	1	;
	23

B’s 1 day’s work =	10	.
	299

(A + B)’s 1 day’s work =		1	+	10		=	23	=	1	.
		23		299			299		13

Therefore, A and B together can complete the work in 13 days.

Question: A and B can do a job together in 7 days. A is 1 times as efficient as B. The same job can be done by A alone in :
[A].

9	1	days
	3

[B].

11 days

[C].

12	1	days
	4

[D].

16	1	days
	3

Answer: Option B

Explanation:

(A’s 1 day’s work) : (B’s 1 day’s work) =	7	: 1   =   7 : 4.
	4

Let A’s and B’s 1 day’s work be 7x and 4x respectively.

Then, 7x + 4x =	1	11x =	1	x =	1	.
	7		7		77

A’s 1 day’s work =		1	x 7		=	1	.
		77				11