Time and Work is an important topic asked in banking, railway, insurance and other competitive exams like IBPS Clerk, SBI Clerk, SSC CGL, IBPS PO, SBI PO, CAT, NIACL AO etc. This article is a part of ”Shortcut Techniques’’ series & will help you provide the shortcut method to solve time and work problem. This Time and Work shortcut will solve the Time and work problem quickly & will help you save at least 1 minute per problem.
Time and Work Shortcut – Fraction Conversion
An effective Time and work shortcut trick that will help you to solve the Time and Work problem is this Fraction conversion table. Try to directly remember fraction conversion into percentage. Check some examples given in the table below.
| 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% |
For example, let us suppose that A can do a job in 10 days.
1st method: Fraction Technique
A = 10 days i.e so work done in a day is 1/10th.
2nd Method: Efficiency Technique
Work done by a person in unit time is defined as efficiency in Time and Work Problems
A = 10 days so efficiency of A per day = 100/10 = 10%
Time and Work Shortcut – Time and Work Questions
Now we will go through some examples to understand this time and work shortcut trick closely.
Q1. Anil can do a job in 10 days. Babu can do the same job in 5 days. In how many days they can complete the job if they work together?
- 6 days
- 3.33 days
- 7.25 days
- 7.5 days
- None of these
Ans: 3.33 days
Solution:
Anil can do a job in 10 days,
So efficiency of Anil = 100/10 = 10%
Similarly, Babu’s efficiency = 100/5 = 20%
Combined efficiency of Anil + Babu per day becomes = 20 + 10 = 30%
Now, we have to find out the number of days taken by both Anil and Babu to do 100% work,
Since they can do 30% wok in 1 day,
So, they will 100% work in 100/30 = 3.33 days
NOTE: Efficiencies get added directly!
Q2. Anil and Babu can do a job in 8 days. Babu and Charan can do the same job in 12 days. Anil, Babu and Charan can do the job in 6 days. In how many days Anil and Charan can complete the job?
- 6 days
- 8 days
- 10 days
- 12 days
- None of these
Ans: 8 days
Solution:
Anil and Babu can do a job in 8 days
∴ Combined efficiency of Anil + Babu = 100/8 = 12.5% ………………………………………(1)
Similarly, combined efficiency of Babu + Charan = 100/12 = 8.33%……………………..(2)
Similarly, combined efficiency of Anil + Babu + Charan = 100/6 = 16.66%…………….(3)
So now, if we want to calculate the efficiency of Anil and Charan together, we need to first calculate the individual efficiency of Anil and Charan.
So we first deduct equation 1 from equation 3 to get the efficiency of Charan. Then we deduct equation 2 from equation 3 we will get the efficiency of Anil.
Let’s calculate the efficiency of Charan = (Anil + Babu + Charan) – (Anil + Babu) = 16.66 – 12.5 = 4.16%
In the same way, we calculate the efficiency of Anil = 16.66 – 8.33 = 8.33%
So, combined efficiency of Anil and Charan = 8.33% + 4.16% ≈ 12.5%
∴ They need = 100/12.5 = 8 days
So they can complete the job in 8 days.
NOTE: This method looks long but only because it has been solved with all the steps. When you attempt time and work question in the exam paper, try to solve it directly using this technique, noting down only the figures, while performing all calculations (especially fractions) mentally. You simply need to get into the habit of using this time and work shortcut method, as it is easier to solve mentally. This will save you precious time during the exam.
This Time and work shortcut trick teaches us not to get involved in fractions. Solving fractions takes a lot of time and also there are chances of mistakes.
Faster Now!
Time and Work is an important topic asked in banking, railway, insurance and other competitive exams like IBPS Clerk, SBI Clerk, SSC CGL, IBPS PO, SBI PO, CAT, NIACL AO etc. This article is a part of ”Shortcut Techniques’’ series & will help you provide the shortcut method to solve time and work problem. This Time and Work shortcut will solve the Time and work problem quickly & will help you save at least 1 minute per problem.
Time and Work Shortcut – Fraction Conversion
An effective Time and work shortcut trick that will help you to solve the Time and Work problem is this Fraction conversion table. Try to directly remember fraction conversion into percentage. Check some examples given in the table below.
| 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% |
For example, let us suppose that A can do a job in 10 days.
1st method: Fraction Technique
A = 10 days i.e so work done in a day is 1/10th.
2nd Method: Efficiency Technique
Work done by a person in unit time is defined as efficiency in Time and Work Problems
A = 10 days so efficiency of A per day = 100/10 = 10%
Time and Work Shortcut – Time and Work Questions
Now we will go through some examples to understand this time and work shortcut trick closely.
Q1. Anil can do a job in 10 days. Babu can do the same job in 5 days. In how many days they can complete the job if they work together?
- 6 days
- 3.33 days
- 7.25 days
- 7.5 days
- None of these
Ans: 3.33 days
Solution:
Anil can do a job in 10 days,
So efficiency of Anil = 100/10 = 10%
Similarly, Babu’s efficiency = 100/5 = 20%
Combined efficiency of Anil + Babu per day becomes = 20 + 10 = 30%
Now, we have to find out the number of days taken by both Anil and Babu to do 100% work,
Since they can do 30% wok in 1 day,
So, they will 100% work in 100/30 = 3.33 days
NOTE: Efficiencies get added directly!
Q2. Anil and Babu can do a job in 8 days. Babu and Charan can do the same job in 12 days. Anil, Babu and Charan can do the job in 6 days. In how many days Anil and Charan can complete the job?
- 6 days
- 8 days
- 10 days
- 12 days
- None of these
Ans: 8 days
Solution:
Anil and Babu can do a job in 8 days
∴ Combined efficiency of Anil + Babu = 100/8 = 12.5% ………………………………………(1)
Similarly, combined efficiency of Babu + Charan = 100/12 = 8.33%……………………..(2)
Similarly, combined efficiency of Anil + Babu + Charan = 100/6 = 16.66%…………….(3)
So now, if we want to calculate the efficiency of Anil and Charan together, we need to first calculate the individual efficiency of Anil and Charan.
So we first deduct equation 1 from equation 3 to get the efficiency of Charan. Then we deduct equation 2 from equation 3 we will get the efficiency of Anil.
Let’s calculate the efficiency of Charan = (Anil + Babu + Charan) – (Anil + Babu) = 16.66 – 12.5 = 4.16%
In the same way, we calculate the efficiency of Anil = 16.66 – 8.33 = 8.33%
So, combined efficiency of Anil and Charan = 8.33% + 4.16% ≈ 12.5%
∴ They need = 100/12.5 = 8 days
So they can complete the job in 8 days.
NOTE: This method looks long but only because it has been solved with all the steps. When you attempt time and work question in the exam paper, try to solve it directly using this technique, noting down only the figures, while performing all calculations (especially fractions) mentally. You simply need to get into the habit of using this time and work shortcut method, as it is easier to solve mentally. This will save you precious time during the exam.
This Time and work shortcut trick teaches us not to get involved in fractions. Solving fractions takes a lot of time and also there are chances of mistakes.
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