Time and Work - Shortcuts and Tricks

Trick

One simple technique is using days in denominator while solving questions. For example, A can do a job in 3 days and B can do the same job in 6 days. In how much time they can do the job together.

Solution - 1/3 + 1/6 = 1/2, hence 2 days is the answer.

Examiner can set the question in opposite way and can ask you how much time A or B alone will take to complete the job. It is quite easy to calculate said question by putting values in equation we arrived in above question.

 You need to understand one simple concept - If A can do a job in 10 day then in one day A can do 1/10th of job.

Shortcut

Best trick that I use in exams myself is by finding the efficiency of workers in percent. If A can do a job in 2 days then he can do 50% in a day. 

Number of days required to complete the work	Work that can be done per day	Efficiency in Percent
n	1/n	100/n
1	1/1	100%
2	1/2	50%
3	1/3	33.33%
4	1/4	25%
5	1/5	20%
6	1/6	16.66%
7	1/7	14.28%
8	1/8	12.5%
9	1/9	11.11%
10	1/10	10%
11	1/11	9.09%

Now let's solve questions with this trick

Question - A take 5 days to complete a job and B takes 10 days to complete the same job. In how much time they will complete the job together ?

Solution - A's efficiency = 20%, B's efficiency = 10%. If they work together they can do 30% of the job in a day. To complete the job they need 3.33 days. 

Question - A is twice as efficient as B and can complete a job 30 days before B. In how much they can complete the job together ?

Solution - Let efficiency percentage as x
A's efficiency = 2x and B's efficiency = x
A is twice efficient and can complete the job 30 days before B. So,
A can complete the job in 30 days and B can complete the job in 60 days
A's efficiency = 1/30 = 3.33%
B's efficiency = 1/60 = 1.66%   
Both can do 5% ( 3.33%  + 1.66% ) of the job in 1 day.
So the can complete the whole job in 20 days (100/5)

Question - A tank can be filled in 20 minutes. There is a leakage which can empty it in 60 minutes. In how many minutes tank can be filled?

Solution -
Method 1 ⇒ Efficiency of filling pipe = 20 minutes = 1/3 hour = 300%
⇒ Efficiency of leakage = 60 minutes = 100%
We need to deduct efficiency of leakage so final efficiency is 200%. We are taking 100% = 1 Hour as base so answer is 30 minutes.

Method 2 ⇒ Efficiency of filling pipe = 100/20 = 5%
⇒ Efficiency of leakage pipe = 100/60 = 1.66%
⇒ Net filling efficiency = 3.33%
So tank can be filled in = 100/3.33% = 30 minutes

You can change the base to minutes or even seconds.

You can solve every time and work question with this trick. In above examples I wrote even simple calculations. While in exams you can do these calculations mentally and save lots of time.  

Comment below in case of any query, I promise to reply within 24 hours.


Question - 4 men and 6 women working together can complete the work within 10 days. 3 men and 7 women working together will complete the same work within 8 days. In how many days 10 women will complete this work ?

Solution - Let number of men =x, number of women = y
⇒ Efficiency of 4 men and 6 women = 100/10 = 10%
⇒ so, 4x+6y = 10
Above equation means 4 men and 6 women can do 10% of a the job in one day.
⇒ Efficiency of 3 men and 7 women = 100/8 = 12.5%
so, 3x+7y = 12.5
By solving both equations we get, x = -0.5 and y = 2
⇒ Efficiency of 1 woman(y) = 2% per day
⇒ Efficiency of 10 women per day = 20%
So 10 women can complete the job in 100/20 = 5 days

Question - A and B together can complete a task in 20 days. B and C together can complete the same task in 30 days. A and C together can complete the same task in 30 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of days taken by C when completing the same task alone?

Solution -  ⇒ Efficiency of A and B = 1/20 per day = 5% per day ________________1
⇒ Efficiency of B and C = 1/30 per day = 3.33% per day______________2
⇒ Efficiency of C and A = 1/30 per day = 3.33% per day______________3
Taking equation 2 and 3 together
⇒ B + C = 3.33% and C + A = 3.33%
⇒ C and 3.33% will be removed. Hence A = B
⇒ Efficiency of A = B = 5%/2 = 2.5% = 1/40
⇒ Efficiency of C = 3.33% - 2.5% = 0.833% = 1/120
⇒ A can do the job in 40 days and C can do the job in 120 days he they work alone.
⇒  Ratio of number of days in which A and C can complete the job 1:3. 

Time, Speed and Distance: Concepts and Problems

Today I am going to discuss a very important

Concepts

1) There is a relationship between speed, distance and time:

Speed = Distance / Time OR

Distance = Speed* Time

2) Average Speed = 2xy / x+y

where x km/hr is a speed for certain distance and y km/hr is a speed at for same distance covered.

Remember that average speed is not just an average of two speeds i.e. x+y/2. It is equal to 2xy / x+y

3) Always remember that during solving questions units must be same. Units can be km/hr, m/sec etc.

Conversion of km/ hr to m/ sec and m/ sec to km/ hr
x km/ hr = (x* 5/18) m/sec i.e. u just need to multiply 5/18
Similarly, x m/sec = (x*18/5) km/sec


4) As we know, Speed = Distance/ Time. Now, if in questions Distance is constant then speed will be inversely proportional to time i.e. if speed increases ,time taken will decrease and vice versa.

Time and Distance Problems

Problem 1: A man covers a distance of 600m in 2min 30sec. What will be the speed in km/hr?

Solution: Speed =Distance / Time
⇒ Distance covered = 600m, Time taken = 2min 30sec = 150sec
Therefore, Speed= 600 / 150 = 4 m/sec
⇒ 4m/sec = (4*18/5) km/hr = 14.4 km/ hr.

Problem 2: A boy travelling from his home to school at 25 km/hr and came back at 4 km/hr. If whole journey took 5 hours 48 min. Find the distance of home and school.

Solution: In this question, distance for both speed is constant.
⇒ Average speed = (2xy/ x+y) km/hr, where x and y are speeds
⇒ Average speed = (2*25*4)/ 25+4 =200/29 km/hr
Time = 5hours 48min= 29/5 hours
Now, Distance travelled = Average speed * Time
⇒ Distance Travelled = (200/29)*(29/5) = 40 km
Therefore distance of school from home = 40/2 = 20km.

Problem 3: Two men start from opposite ends A and B of a linear track respectively and meet at point 60m from A. If AB= 100m. What will be the ratio of speed of both men?

Solution: According to this question, time is constant. Therefore, speed is directly proportional to distance.

Speed∝Distance


⇒ Ratio of distance covered by both men = 60:40 = 3:2
⇒ Therefore, Ratio of speeds of both men = 3:2

Problem 4: A car travels along four sides of a square at speeds of 200, 400, 600 and 800 km/hr. Find average speed.

Solution: Let x km be the side of square and y km/hr be average speed
Using basic formula, Time = Total Distance / Average Speed
x/200 + x/400 + x/600 + x/800 = 4x/y ⇒ 25x/ 2400 = 4x/ y⇒ y= 384

⇒ Average speed = 384 km/hr topic Time, Speed and Distance.

Postal Assistant Exam 2014 Model Questions from Mathematics Section

1. If 37% of a number is 990.86, what will be approximately the 19% of that number
(A) 600
(B) 400
(C) 500
(D) 700

2. A number, on subtracting 15 from it, reduces to its 80%.What is 40% of that number?
(A) 60
(B) 45
(C) 30
(D) 90

3. If ¾ of the number is 40 more than 40% of the same number.What is the number:
(A) 100
(B) 150
(C) 200
(D) 400

4. In library, 20% books are in hindi, 50% of the remaining in English and the remaining 9000 are in various other languages. What is the total number of books in english ?
(A) 4000
(B) 3000
(C) 2250
(D) None of these

5. Avinash spends 30% of his income on scooter petrol, ¼ of the remaining on house rent and balance on food. If he spends Rs 300 on petrol, Then what is the expenditure on house rent?
(A) 525
(B) 1000
(C) 675
(D) 175

6. 35% of 30 = 25% of ? +1
(A) 28
(B) 38
(C) 42
(D) 32

7. ? of 6144 = 2 ½ x 245.76
(A) 16
(B) 20
(C) 5
(D) 10

8. 12.5 of 192 = 50% of ?
(A) 48
(B) 96
(C) 24
(D) None

9 45% of ? + 30% of 90 = 30% of 210
(A) 120
(B) 80
(C) 60
(D) 90

10. one fourth of one third of two fifth of a number is 15. What will be 40% of that number?
(A) 120
(B) 350
(C) 270
(D) 180

11. If the cost price of 12 tables is equal to 16 tables, the loss % is
(A) 15
(B) 20
(C) 25
(D) 30

12. A man buys oranges at Rs 5 a dozen and an equal number at Rs 4 a dozen. He sells them at Rs 5.50 a dozen and makes a profit of Rs 50. How many dozens of oranges he buy?
(A) 30
(B) 40
(C) 50
(D) 60

13. Ajay bought 15 Kg dal at Rs 14.50 per Kg and 10 Kg at rate of Rs 13 per Kg. he mixed the two & sold the mixture at rate of Rs 15 per Kg. What is total gain in Rs
(A) 1.10
(B) 16.50
(C) 11
(D) 27.50

14. A producer of tea blends two varieties of two tea gardens one costing Rs18 per Kg and other Rs20 per Kg in ratio of 5:3. If he sell the blended at Rs21 per Kg, The gain % is?
(A) 10
(B) 12
(C) 19
(D) 22

15. Gopal purchased 35 Kg rice at Rs 9.5o per Kg & 30 Kg at rate of Rs 10.50. He mixed the two. Approximately at what price per Kg should he sell the mixture to make 35% profit
(A) 12
(B) 12.50
(C) 13
(D) 13.50

16. A profit of Rs 30000 is to be distributed among A,B & C in the proportion of 3:5:7. What will be the difference in B & C share?
(A) 2000
(B) 4000
(C) 10000
(D) 14000

17.A certain amount was devided between salim & Rahimin ratio of 4:3. If Rahim share was Rs 2400, The total amount was
(A) 5600
(B) 3200
(C) 9600
(D) 16800

18 A box contain Rs56 in form of coinsof one rupee, 50 paisa, 25 paisa. The 50 paisa coins are double of 25 paisa coins and 4 times the number of one rupee coins. How many 50 paisa coins are there in the box ?
(A) 64
(B) 32
(C) 16
(D) data inadequate

19. In a school 105 of the boys are same in number as ¼th of the girls and 10% of the girls are same in number as 1/25th of boys. What is the ratio of boys & girls in the school ?
(A) 3:2
(B) 5:2
(C) 2:1
(D) 4:3

20. The marks obtain by Praveen & Vijay are in 4:5& obtain by Vijay & Suresh are in ratio of 3:2. The marks obtain by Praveen & Suresh are in ratio of ?
(A) 2:1
(B) 5:3
(C) 6:5
(D) 5:6

Answers : 

 1. (C) 2. (C) 3. (C) 4. (D) 5. (D) 6. (B) 7. (D) 8. (A) 9. (B) 10. (D)
11. (B) 12. (V) 13. (D) 14. (B) 15. (D) 16. (B) 17. (A) 18. (A) 19. (B) 20. (C)

Train Problems for PA/SA Exams

1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
A. 120 metres         B. 180 metres
C. 324 metres   D. 150 metres


2.A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

A. 45 km/hr B. 50 km/hr
C. 54 km/hr D. 55 km/hr  


3.The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
A. 200 m B. 225 m
C. 245 m D. 250 m



4. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
A. 1 : 3   B. 3 : 2
C. 3 : 4   D. None of these


5.A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A. 120 m B. 240 m
C. 300 m D. None of these






6. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
A. 65 sec B. 89 sec
C. 100 sec D. 150 sec


7. Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:
A. 50 m      B. 72 m
C. 80 m      D. 82 m



8.A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
A. 40 sec B. 42 sec
C. 45 sec D. 48 sec



9. Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:
A. 36 B. 45
C. 48 D. 49



10. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
A. 3.6 sec B. 18 sec
C. 36 sec D. 72 sec

APTITUDE TEST- DECEMBER 2009

 PART 1 – ENGLISH
( Select the most appropriate word/set of words)

1.  The word most nearly opposite in meaning to Valor
a.   admonition 
b.    Injustice        
c.   Cowardice    
d .  Generosity

2.   The word most nearly similar in meaning to tentative
a.   Prevalent      
b.   Portable      
c.   Making        
d.  Experimental

3.  The pair whose relationship is most  like  the relationship expressed in the pair  beggar: beg
a.     Medium- Advise             
b.    Mediator: Disagree 
C.    Mercenary : Demand      
d.    Mentor : Guide

Fill in the Blanks   (  Question  4-10 )
4.   We list confidence in him because he never ------------------his promise.
5.   Her true feelings  --------------- themselves in her sarcastic asides; only then  was  her ------------- revealed

6.   Technically glass is a mineral and ---------------
a.    Water so      
b.    water is so     
c.    so is water     
d.    so water is

7.   Rajasthan   --------------- a very climate
a.     ha
b.    being                 
c.     having               
d.    with

8   One of   the  least effective ways of storing information is leaning
a. how repeat              
b. repeating   
c. to repeat    
d. Repeat

9     Many modern architects insist on------------------ materials native to the region
      that will blend in to surroundings landscape .
a. use             
b. to use                
c. the use           
d. using

10.  By the  time a baby has reached its first birthday , he should , without the help of  an 
      adult ----------------- sit up or even stand up.
a. to be able      
b. able to          
c. to be able      
d. be able to

PART II: MATHEMATICS
11.     A jar contains 10 red marbles and 30 green Ones. How many red marbles must   be added to the jar so that 60 % of the marbles will be red?

a.    25                
b.    30               
c.     35                      
d.     40

12.    Driving at 48 miles per hour, how many minutes will take to drive 32miles.
a.   23        
b    32         
c.    40        
d.    45         
             
13.    If  a = 9*8321 and b=9*7321 what is the value of a –
a.    8000        
b.   9000                
c.    7000             
d. 6000

14.    From 1989 to 1990, the number of applicants to a college increased 15 % to 5000.
          How many applications were there in 1989?
a. 759           
b. 4301         
c. 4400              
d. 5819

15.   Find two numbers whose sum is 27 and product is 182
a.   11, 12         
b.   12, 13           
c.   13, 14   
d.   14, 15

16.   How many three- digit numbers are divisible by 7 ?
a.    108         
b.   118.            
c.   128 
d.  138

17    Liz is now twice as old as Jose but 6 years ago she was 5 times as old as he was.       How old Liz now?
a. 10           
b. 16           
c. 20                
d. 24

18.    What is the sum of the product and quotient of 8 and 8 ?
a.   62        
b.   63             
c.   64            
d .  65

19. Liz  solved   24  Maths problems in 15 minutes.  At this rate, how many problems can she solve in 40 minutes?
a.    25        
b.   64           
c.    40      
d.   48

20.    If the average (arithmetic mean) of 25,31 and x is 37 what is the value of  x?
a.     31      
b.    37               
c.     43                
d.    55