Time and Work - General Questions

A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?

A.	30 days
B.	40 days
C.	60 days
D.	70 days

Answer: Option C

Explanation:

Let A's 1 day's work = x and B's 1 day's work = y.

Then, x + y =	1	and 16x + 44y = 1.
	30

Solving these two equations, we get: x =	1	and y =	1
	60		60

B's 1 day's work =	1	.
	60

Hence, B alone shall finish the whole work in 60 days.

A and B can do a job together in 7 days. A is 1 1-div-3by4 times as efficient as B. The same job can be done by A alone in :

A.	9 1/3 days
B.	11 days
C.	12 1/4 days
D.	16 1/3 days

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

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 1/3 days
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

A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:

A.	5 days
B.	6 days
C.	10 days
D.	10 1/2 days

Answer: Option C

Explanation:

(B + C)'s 1 day's work =		1	+	1		=	7	.
		9		12			36

Work done by B and C in 3 days =		7	x 3		=	7	.
		36				12

Remaining work =		1 -	7		=	5	.
			12			12

Now,	1	work is done by A in 1 day.
	24

So,	5	work is done by A in		24 x	5		= 10 days.
	12				12

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

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)

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.

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

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