## About Time and Work

This post is a part of “Shortcut Techniques” series where I decided to share shortcut techniques related quantitative techniques that can be used in IBPS exam or any other competitive exam.

Time and work is an important topic in IBPS exams, including clerks, PO and specialist officers.

## 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

Number of daysrequired 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 –**

**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** –

**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%

( As Shobhna and Aswin are facing problem in solving this question, I am solving this question with second method which is also very easy, hope this will make the solution lot easier.)

**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

**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 –**

**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.