Does alone a work in 4 days B does alone a work in 8 days in how many days the work will be completed if A & B work together?

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Exercise :: Time and Work - General Questions
Exercise :: Time and Work - General Questions
Exercise :: Time and Work - General Questions
Exercise :: Time and Work - General Questions
Exercise :: Time and Work - General Questions

In how many days can a work be completed by A and B together?I. A alone can complete the work in 8 days.II. If A alone works for 5 days and B alone works for 6 days, the work gets completed.III. B alone can complete the work in 16 days.A. II and either I or IIIB. Any two of the threeC. I and IID. II and III

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Exercise :: Time and Work - General Questions

11.

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?

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

12.

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?

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.

Page 2

Exercise :: Time and Work - General Questions

16.

X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

A.	6 days
B.	10 days
C.	15 days
D.	20 days

Answer: Option B

Explanation:

Work done by X in 4 days =		1	x 4		=	1	.
20	5

Remaining work =		1 -	1		=	4	.
5	5

(X + Y)'s 1 day's work =		1	+	1		=	8	=	2	.
20	12	60	15

Now,	2	work is done by X and Y in 1 day.
15

So,	4	work will be done by X and Y in		15	x	4		= 6 days.
5	2	5

Hence, total time taken = (6 + 4) days = 10 days.

17.

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.
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.

18.

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

Page 3

Exercise :: Time and Work - General Questions

21.

A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:

A.	4 days
B.	6 days
C.	8 days
D.	12 days

Answer: Option B

Explanation:

Suppose A, B and C take x,	x	and	x	days respectively to finish the work.
2	3

Then,		1	+	2	+	3		=	1
x	x	x	2

	6	=	1
x	2

x = 12.

So, B takes (12/2) = 6 days to finish the work.

22.

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.

23.

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

Page 4

Exercise :: Time and Work - General Questions

26.

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

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

27.

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.

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

28.

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.
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

Page 5

Exercise :: Time and Work - General Questions

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.

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.

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: