Time and Work - General Questions (3)

17.

P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?

A.	5 5/11
B.	5 6/11
C.	6 5/11
D.	6 6/11

Answer: Option A

Explanation:

P can complete the work in (12 x 8) hrs. = 96 hrs.

Q can complete the work in (8 x 10) hrs. = 80 hrs.

P's1 hour's work =	1	and Q's 1 hour's work =	1	.
	96		80

(P + Q)'s 1 hour's work =		1	+	1		=	11	.
		96		80			480

So, both P and Q will finish the work in		480		hrs.
		11

Number of days of 8 hours each =		480	x	1		=	60	days = 5	5	days.
		11		8			11		11

18.

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.

19.

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.

20.

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

21.

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.

22.

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

23.

A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:

A.	15 days
B.	20 days
C.	25 days
D.	30 days

Answer: Option C

Explanation:

(A + B)'s 1 day's work =	1
	10

C's 1 day's work =	1
	50

(A + B + C)'s 1 day's work =		1	+	1		=	6	=	3	. .... (i)
		10		50			50		25

A's 1 day's work = (B + C)'s 1 day's work .... (ii)

From (i) and (ii), we get: 2 x (A's 1 day's work) =	3
	25

A's 1 day's work =	3	.
	50

B's 1 day's work		1	-	3		=	2	=	1	.
		10		50			50		25

So, B alone could do the work in 25 days.

24.

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

Therefore B alone will take 12 hours to do the work.

Time and Work - General Questions (3)

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