TIME AND WORK

1. 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.
   EXAMPLES
   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

   
   

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APTITUDE QUESTIONS

1.PROBLEMS IN TRAINS km/hr to m/s conversion: a km/hr = a x 5 m/s. 18 m/s to km/hr conversion: a m/s = a x 18 km/hr. 5 Formulas for finding Speed, Time and Distance Time taken by a train of length l metres to pass a pole or standing man or a signal post is equal to the time taken by the train to cover l metres. Time taken by a train of length l metres to pass a stationery object of length bmetres is the time taken by the train to cover (l + b) metres. Suppose two trains or two objects bodies are moving in the same direction at um/s and v m/s, where u > v, then their relative speed is = (u - v) m/s. Suppose two trains or two objects bodies are moving in opposite directions at um/s and v m/s, then their relative speed is = (u + v) m/s. If two trains of length a metres and b metres are moving in opposite directions atu m/s and v m/s, then: The time taken by the trains to cross each other = (a + b) sec. (u + v) If two trains of length a metres and b metres are moving in the same direction atu m/s and v m/s, then: The time taken by the faster train to cross the slower train = (a + b) sec. (u - v) If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a)

1.	A train 100 m long is running at the speed of 30 km/hr. Find the time taken by it to pass a man standing near the railway line.
	A.   10 sec.	B.   12 sec.
	C.   14 sec.	D.   16 sec.

Solution

Speed of the train = (30 x 5/18)m/sec = (25 / 3) m/sec. Distance moved in passing  the standing man = 100 m. Required time taken = 100 /( 25 / 3) =(100 x 3 / 25) sec = 12 sec.

2.	A man sitting in a train which is travelling at 50 kmph observes that a goods train, travelling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.
	A.   52 kmph.	B.   62 kmph.
	C.   72 kmph.	D.   80 kmph.

Solution

Relative Speed = (280 / 9)m/sec = (280/9 x 18/5) = 112 kmph. Speed of the train = (112 - 50)kmph = 62 kmph.

3.	A train 150 m long is running with a apecd of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going?
	A.   6sec.	B.   7sec.
	C.   9sec.	D.   11sec.

Solution

Speed of the train relative to man =( 68 - 8 ) = 60 Kmph = 60 x 5 / 18 =50/3 m/sec. Time taken by it to cover 150 m at (50 /3)m/sec = (112 - 50)kmph = (150 x 3/50)sec = 9 sec.

4.	A train moves with a speed of 108 kmph.Its speed in metres per second is
	A.  10.8	B.  18
	C.  30	D.  38.8

Solution

Speed = 108 Kmph = (108 x 5/18)m/sec = 30 m/sec.

5.	Two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 8 seconds. The length of the faster train is
	A.  80 m	B.  100 m
	C.  120 m	D.  180 m

Solution

Relative Speed = (36 + 45) km/hr = (81 x 5/18) m/sec = (45/2) m/sec Length of the train = (45 / 2 x 8) m = 180 m.

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