DAILY EXERCISES: TIME AND WORK

Thursday, 5 February 2015

TIME AND WORK

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Work from Days:

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

n
Days from Work:

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

n

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.

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#2

(M1D1HI)/ W1 = (M2D2H2)/W2

Where M1 & M2 represents no of labourers; D1 & D2 represents no of days; H1 & H2 represents no of hours; W1&W2 represents work done.

If there are 2 persons A & B such that A can do work in ‘a’ days and B can do work in ‘b’days.
Such that ‘a’ is a multiple of ‘b’, then, time taken by them to complete the work together = Bigger no/Sum of ratios

Eg: A can do work in 9 days, B can do work in 18 days. In how many days they will complete
the work together.
Bigger no=18, Ratio=9:18=1:2
No of days = 18/(1 + 2)
= 6 days

If ‘a’ is not a multiple of ‘b’, then time taken by A&B to complete the work together
= (LCM)/(Sum of ratios)

Eg: A can do a piece of work 30 days. B can do work in 45 days. In how many days they will
complete the work together?

LCM = 90, Ratio= 30:45=2:3
No of days= 90/(2 + 3) = 90/5

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If there are 3 persons A, B & C whose time taken a,b,c days respectively, to complete a certain
work. Time taken by them to complete the work = LCM of (a, b, c)/(LCM/a + LCM/b + LCM/c)

Note: For 3 persons the common format is
Step1: Find the LCM

Step2: Find the individual share of work i.e. LCM/a, LCM/b, LCM/c.

Step3: Rest methods depend on the question i.e. follow the question patterns.

Eg: A, B and C can do a work in 15,20,45 days respectively. In how many days they can
complete the work together.

LCM=180

No of days= [180/ (180/15 + 180/20 + 180/45)
= [180/ (12+9+4)]
= [180/25]
= 7.2 days

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Fastest Finger First

A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was

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Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank in gallons is

	A.	100
	B.	110
	C.	120
* #6 ********* Pipes & Cisterns If there are 2 pipes A & B such that A (inlet pipe) & B (outlet pipe). Such that A can fill tank in ‘a’ minutes and B can empty the tank in ‘b’ minutes , then time taken to fill the tank if both are operated together = Bigger no/Difference of ratios Eg: A can fill tank in 9 minutes, B can empty the tank in 18 minutes.. In what time the tank be filled, if both pipes work simultaneously? Bigger no=18, Ratio=9:18=1:2 Time taken to fill the tank = 18/(2 1) = 18 minutes If ‘a’ is not a multiple of ‘b’, then time taken by A&B to fill the tank. = (LCM)/(Difference of ratios) Eg.: An inlet pipe can fill the tank in 30 minutes. B an outlet pipe can empty the tank in 45 minutes. In what time the tank be filled if both pipes work simultaneously? Time taken to fill the tank= LCM = 90 = Ratio= 30:45=2:3 = 90/(3 2) = 90/1 = 90 minutes If there are 3 pipes A, B & C, in which A, B are inlet pipes which takes a,b,minutes respectively to fill the tank and C an outlet pipe which takes c minutes to empty the tank	D.	140 ****