Time and Work  Aptitude basics, practice questions, answers and explanations 
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Time & Work
 

(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 = 18

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
 

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

Time taken by them to fill the tank, if all of them are operated together.

= LCM of abc/ (LCM/a + LCM/b - LCM/c)

Eg: A, B two inlet pipes takes 15,18 minutes to fill the tank and C an oulet pipe takes 45 minutes to empty the tank respectively. In what time the tank be filled if all of them are operated together?

LCM=90
No of days= [90/(90/15 + 90/18 - 90/45)
               =  [90/(6+5-2)]                    
               =  [90/9]
               = 10 minutes

Note: In case of division of money with respect to share of each person’s work then share of A = bc/ab+bc+ac

In case of division of money with respect to share of each person’s work then share of B = ac/ab+bc+ac
In case of division of money with respect to share of each person’s work then share of C = ab/ab+bc+ac

Same as Share of A:(LCM/a)/ (LCM/a + LCM/b + LCM/c)
              Share of B:(LCM/b)/ (LCM/a + LCM/b + LCM/c)
              Share of C:(LCM/c)/ (LCM/a + LCM/b + LCM/c)

                                 
Eg: A,B,C can do a work in 15,20,45 days respectively. They get Rs 500 for their work. What is the share of A?

LCM = 180

Share of A = (LCM/a x Total amount)/LCM/a + LCM/b + LCM/c

                =  (180/15)/(180/15 +180/20 + 180/45)

                = (12/25) * 500

                =  Rs.240
 

Exercise questions
 

1. Two workers A and B manufactured a batch of identical parts. A worked for 2 hours and B worked for 5 hours and they did half the job. Then they worked together for another 3 hours and they had to do (1/20)th of the job. How much time does B take to complete the job, if he worked alone?
A) 24 hours 
B) 12 hours 
C) 15 hours 
D) 30 hours

2. Pipe A can fill a tank in 'a' hours. On account of a leak at the bottom of the tank it takes thrice as long to fill the tank. How long will the leak at the bottom of the tank take to empty a full tank, when pipe A is kept closed?
A) (3/2)a hours             
B) (2/3)a              
C) (4/3)a               
D) (3/4)a

3. A and B working together can finish a job in T days. If A works alone and completes the job, he will take T + 5 days. If B works alone and completes the same job, he will take T + 45 days. What is T?
A) 25  
B) 60           
C) 15            
D) None of these

4. A man can do a piece of work in 60 hours. If he takes his son with him and both work together then the work is finished in 40 hours. How long will the son take to do the same job, if he worked alone on the job?
A) 0 hours 
B) 120 hours 
C) 24 hours   
D) None of these

5. A, B and C can do a work in 5 days, 10 days and 15 days respectively. They started together to do the work but after 2 days A and B left. C did the remaining work (in days)
A) 1    
B) 3             
C) 5             
D) 4

6. X alone can do a piece of work in 15 days and Y alone can do it in 10 days. X and Y undertook to do it for Rs.720. With the help of Z they finished it in 5 days. How much is paid to Z?
A) Rs.360 
B) Rs.120 
C) Rs.240 
D) Rs.300

7. Ram starts working on a job and works on it for 12 days and completes 40% of the work. To help him complete the work, he employs Ravi and together they work for another 12 days and the work gets completed. How much more efficient is Ram than Ravi?
A)50%
B) 200%  
C) 60%            
D)100%

8. A red light flashes 3 times per minute and a green light flashes 5 times in two minutes at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour?
A) 30 
B) 24              
C) 20              
D) 60

9. A and B can do a piece of work in 21 and 24 days respectively. They started the work together and after some days A leaves the work and B completes the remaining work in 9 days. After how many days did A leave?
A) 5    
B) 7                
C) 8                
D) 6

10. Ram, who is half as efficient as Krish, will take 24 days to complete a work if he worked alone. If Ram and Krish worked together, how long will they take to complete the work?
A) 16 days 
B) 12 days  
C) 8 days  
D) 18 days

Answer Key

1.C; 2.A; 3.C; 4.B;5.D; 6.B; 7.D; 8.A; 9.B; 10.C