Time And Work Full Exercise For All Exams : Only Frequently Asked Questions, Solution And Trick Part-1

IMPORTANT BASIC FORMULAS FOR TIME AND WORK:

1. Work from Days:

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

2. Days from Work:

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

3. Ratio:
   If A is thrice as good a workman as B, then:
   Ratio of work done by A and B = 3 : 1.
   Ratio of times taken by A and B to finish a work = 1 : 3

Question for practice(LEVEL-1: Easy):

1.	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

2.	A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
	A. 9 1 days 5 B. 9 2 days 5 C. 9 3 days 5 D. 10

Answer: Option C

Explanation:

(A + B + C)'s 1 day's work =	1	,
	4

A's 1 day's work =	1	,
	16

B's 1 day's work =	1	.
	12

C's 1 day's work =	1	-		1	+	1		=		1	-	7		=	5	.
	4			16		12				4		48			48

So, C alone can do the work in

48

= 9

3

days.

3.	A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
	A. 12 days B. 15 days C. 16 days D. 18 days

Answer: Option B

Explanation:

A's 2 day's work =		1	x 2		=	1	.
		20				10

(A + B + C)'s 1 day's work =		1	+	1	+	1		=	6	=	1	.
		20		30		60			60		10

Work done in 3 days =		1	+	1		=	1	.
		10		10			5

Now,	1	work is done in 3 days.
	5

 Whole work will be done in (3 x 5) = 15 days.

4.	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

5.	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

6.	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.

7.	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.

8.	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.