Most of the competitive exams like 11 plus have seen the trend of testing students' ability to apply concepts to real problems. This is very evident from the question with situation from daily life. One of such categories of questions is on time and work concept.
In our daily lives, we come across so much work that needs to be completed within a specific time period. Usually, some persons are specifically designated to do these works. What will we do, if after some time we realize that the above said work would not be completed in the desired time? We assign more guys to help the earlier people and finish the work in time. This makes the very basic concept of time and work i.e. more people finish the work in lesser time, and lesser persons take more time to finish work.
Let us assume a wall has to be built which has to be done in 10 days. If a person can build a wall in 10 days, then in 1 day he will build 1/10th of that wall. This basic approach can be applied to solve most of the time and work problems.
Combined formula for Time and Work
Another important concept that is used in time work problems is the combined efficiency of two or more persons. In questions on time and work, the rates at which certain persons or machines work alone are usually given, and it is necessary to compute the rate at which they work together (or vice versa).
Let us say, for example, it takes 3 & 6 hours for Jack and Jill, respectively, to break a dam working alone. So, in 1 hour Jack would have broken one-third or 1/3rd or 33% of the dam and Jill would have broken one-sixth or 1/6th or 16.67% of the dam. In 2 hours, Jack would have destroyed 1/3*2 or 33% *2 = 66.66% of the dam and Jill would have destroyed 1/6th *2= 1/3= 33.33% of the dam. So if Both Jack and Jill work together, they would have destroyed 66.66+ 33.33 (2/3+1/3) or 100% of the dam in 2 hours. Therefore, if both worked together for 1 hour, they would have destroyed 1/3 + 1/6= ½ or half of the dam. Thus in 2 hours, the dam is destroyed.
Generalizing, we conclude that in 1 hour, Jack does 1/r of the job, Jill does 1/s of the job, and Jack & Jill together do 1/h of the job or that together they can finish the job in 'h' hours where the formula for work comes out as 1/r + 1/s = 1/h.
Time and Work Problems Tricks: LCM Approach
The same concept can be learned with unit's work approach as well, which assumes the total work to be done as the LCM (Learn how to calculate LCM) of the number of days taken by each of the persons to complete the work. Let's assume that Nasir can do a piece of work in 20 days working alone and Sophia can do it in 30 days of his own. Now in the above-mentioned case, let us assume that the work consists of the LCM of 20 & 30 i.e. 60 units to be done by Nasir & Sophia. Since Nasir completes 60 units in 20 days, so he completes 60/20 = 3 units of work per day. Similarly, Sophia completes 60 units of the work in 30 days, so he completes 60/30 = 2 units per day. They are doing the same work together, so they do 3 + 2 = 5 units per day. So, 60 units will be done in 60/5 = 12 days.
You should go through the following time and work examples in order to understand the concept better. This is one of the favourite areas of the examiner. You will see aptitude questions on time and work in almost all the competitive examinations. Go through the following Examples to learn the concept of work and time and try to understand the time work questions.
Example 1: Sam can do a job in 30 days. In how many days can he complete 70% of the job?
Sol: Now as per the question he finishes the work in 30 days, or he can do 100% of the work in 30 days. If he has to do only 70% of the work, he will require 70% of the time.
Number of days required = 30 × 70/100 = 21 days.
Example 2: Rozy can do 75% job in 45 days. In how many days can she complete the job?
Sol: Every work is 100% in itself. Rozy does 75% of the work in 45 days. That means she does 1% of the work in 45/75 days and she will do 100% of the work in 100 × 45/75 = 60 days.
Example 3: John can do a piece of work in 60 days; he will do how much of the work in 40 days?
Sol: In 1 day, John does 1/60th of the work, so in 40 days he will do 40 × 1/60 = 2/3rd of the work.
Example 4: Andy can finish a piece of work in 30 days. He will finish what percent of the work in 15 days?
Sol: In 1 day, he does 1/30th of the work, and in 15 days, he will do 15/30th of the work which is 100 × 1530 = 50%.
Example 5: Ria can do a piece of work in 40 days, she will take how many days to finish three-fourth of the work?
Sol: Ria can complete the work in 40 days. She will do ¾th of the work in ¾th of the total time. i.e. she will need 40 × 3/4 = 30 days.
Some more examples
Try to solve the following time and work questions using time and work formula:
Q.1. Raj is twice as efficient as Sally and can finish a piece of work in 25 days less than Sally. Sally can finish this work in how many days?
a) 45 Daysb) 30 Daysc) 90 Daysd) 25 Days e) 50 Days
Answer & Explanation
Sol : Option E
Explanation: Work Formula: Efficiency of Raj: Efficiency of Sally = 2: 1.
Rai will take 1/2 of time as compared to Sally.
Say, Sally takes 2x days and Raj takes x days. Therefore, 2x - x = 25 => x = 25.
Therefore, Sally takes 25 × 2 = 50 days to do the work.
Q.2. A can do a piece of work in 10 days, and B can do the same work in 20 days. With the help of C, they finished the work in 4 days. C can do the work in how many days, working alone?
a) 10 Daysb) 20 Daysc) 30 Daysd) 40 Days e) 50 Days
Answer & Explanation
Sol : Option A
Explanation: C alone will take 1/4 - 1/10 - 1/20 = 2/20 = 1/10 => 10 days to complete the work.
Q.3. Daisy is thrice as efficient as Mary and together they can finish a piece of work in 60 days. Mary will take how many days to finish this work alone?
a) 80 Daysb) 160 Daysc) 240 Daysd) 320 Days e) 400 Days
Answer & Explanation
Sol : Option C
Explanation: Daisy is thrice as efficient as Mary. Let, Mary takes 3x days and Chetan takes x days to complete the work. So 1/x + 1/3x = 1/60 => x = 80. So, Mary will take 80 × 3 = 240 days to complete the work.
Q.4.Mr. David has a sum of money, which is enough to pay Stanley's wages for 30 days and Monika's wages for 60 days. If he employs them together, the money is enough to pay their wages for how many days?
a) 12 Daysb) 10 Daysc) 30 Daysd) 20 Days e) 36 Days
Answer & Explanation
Sol : Option D
Explanation: The concept is the same here as the normal time and work problems. Stanley's one day's wage bill is 1/30 of the total money. Monika's wage bill is 1/60 of the total money. That means together their wage bill is 1/30 + 1/60 = 3/60 = 1/20 of the total money. Thus, the money is enough for their 20 days' wages.
Q.5.X can do a piece of work in 20 days. He worked at it for 5 days and then Y finished it in 15 days. In how many days can X and Y together finish the work?
a) 10 Daysb) 15 Daysc) 18 Daysd) 24 Days e) 32 Days
Answer & Explanation
Sol : Option A
Explanation: X's five day work = 5/20 = 1/4. Remaining work = 1 - 1/4 = 3/4.
This work was done by Y in 15 days. Y does 3/4th of the work in 15 days, he will finish the work in 15 × 4/3 = 20 days. \ X & Y together would take 1/20 + 1/20 = 2/20 = 1/10 i.e. 10 days to complete the work.
Q.6.X can do a piece of work in 30 days. Y can do it in 20 days, and Z can do it in 24 days. In how many days will they all do it together?
a) 6 Daysb) 5 Daysc) 4 Daysd) 4 2/3 Days e) 8 Days
Answer & Explanation
Sol : Option E
Explanation: They all will take 1/30 + 1/20 + 1/24 = 1/8. => 8 days to complete the work
Q.7.M and N can do a piece of work in 8 days and O can do it in 24 days. In how many days will M, N, and O do it together?
a) 6 Daysb) 5 Daysc) 4 Daysd) 4 2/3 Days e) 3 Days
Answer & Explanation
Sol : Option A
Explanation: They will together take 1/8 + 1/24 = 1/6 => 6 days to finish the work.
Q.8.One man can paint a house in, '10' days and another man can do it in 15 days. If they work together, they can do it in 'd' days, then the value of 'd' is
a) 6 Daysb) 8 Daysc) 12 Daysd) 10 Days e) 3 Days
Answer & Explanation
Sol : Option A
Explanation: Total time is d when they are working together = 1/10 + 1/15 = 1/6. => 6 days to complete the work.
Q.9.A can do a piece of work in 9 days and B in 18 days. They begin together, but A goes away three days before the work is finished. The work lasts for
a) 6 Daysb) 8 Daysc) 12 Daysd) 10 Days e) 3 Days
Answer & Explanation
Sol : Option B
Explanation: Let the work lasts for x days. B works for x days and A works for x - 3 days. So(x-3)/9 + (x/18) = 1 => x = 8
Q.10.It takes 'h' hours to mow a lawn. In one hour what part of the lawn is mowed?
a) h - 1b) 1 - hc) 1 / hd) h / (1 + h) e) h
Answer & Explanation
Sol : Option C
Explanation: Total time to mow a lawn = h. So In one hour lawn mowed = 1/h.
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