Time And Work

Question:
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

[A].

Rs. 375

[B].

Rs. 400

[C].

Rs. 600

[D].

Rs. 800

Answer: Option B

Explanation:

C’s 1 day’s work =	1	–		1	+	1		=	1	–	7	=	1	.
	3			6		8			3		24		24

A’s wages : B’s wages : C’s wages =	1	:	1	:	1	= 4 : 3 : 1.
	6		8		24

C’s share (for 3 days) = Rs.		3 x	1	x 3200		= Rs. 400.
			24

Question:
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.

Question:
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.

Question:
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	days
	2

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

Question:
Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:

[A].

15

[B].

16

[C].

18

[D].

25

Answer: Option B

Explanation:

Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4.

Suppose Tanya takes x days to do the work.

5 : 4 :: 20 : x    x =		4 x 20
		5

x = 16 days.

Hence, Tanya takes 16 days to complete the work.

Question: A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:

[A].

20 days

[B].

22	1	days
	2

[C].

25 days

[D].

30 days

Answer: Option B

Explanation:

Ratio of times taken by A and B = 1 : 3.

The time difference is (3 – 1) 2 days while B take 3 days and A takes 1 day.

If difference of time is 2 days, B takes 3 days.

If difference of time is 60 days, B takes		3	x 60		= 90 days.
		2

So, A takes 30 days to do the work.

A’s 1 day’s work =	1
	30

B’s 1 day’s work =	1
	90

(A + B)’s 1 day’s work =		1	+	1		=	4	=	2
		30		90			90		45

A and B together can do the work in	45	= 22	1	days.
	2		2

Question:
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.

Question:
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

Question: 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.

Question:
A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:

[A].

1	day
24

[B].

7	day
24

[C].

3	3	days
	7

[D].

4 days

Answer: Option C

Explanation:

Formula: If A can do a piece of work in n days, then A’s 1 day’s work =	1	.
	n

(A + B + C)’s 1 day’s work =		1	+	1	+	1		=	7	.
		24		6		12			24

Formula: If A’s 1 day’s work =	1	,	then A can finish the work in n days.
	n

So, all the three together will complete the job in		24	days	=	3	3	days.
		7				7