The document 12. Time and Work, Quantitative Aptitude, Civil Service Examination,RPSC UPSC Notes | EduRev is a part of the UPSC Course RAS RPSC Prelims Preparation - Notes, Study Material & Tests.

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In these problems the number of persons, quantity of work done and time taken are important factors. Also time taken by a person depends on the efficiency of that person which comes into picture when different people do the work such as women, children do the work alongside the men. The problems related to time and work can be solved by two major approaches â€“ ratio & proportions and unitary method. Let us proceed to find some formulae related to these questions.

**Important Formulas - Time and Work**

- If A can do a piece of work in n days, work done by A in 1 day = 1/n
- If A does 1/n work in a day, A can finish the work in n days
- If M1 men can do W1 work in D1 days working H1 hours per day and M2 men can do W2 work in D2 days working H2 hours per day (where all men work at the same rate), then M1 D1 H1 / W1 = M2 D2 H2 / W2
- If A can do a piece of work in p days and B can do the same in q days, A and B together can finish it in pq / (p+q) days
- If A is thrice as good as B in work, then
- Ratio of work done by A and B = 3 : 1
- Ratio of time taken to finish a work by A and B = 1 : 3

__SOLVED EXAMPLES__

| |

A. 8/15 | B. 7/15 |

C. 11/15 | D. 2/11 |

**Answer :** Option A

**Explanation :**

Amount of work P can do in 1 day = 1/15

Amount of work Q can do in 1 day = 1/20

Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60

Amount of work P and Q can together do in 4 days = 4 Ã— (7/60) = 7/15

Fraction of work left = 1 â€“ 7/15= 8/15

| |

A. 12 hours | B. 6 hours |

C. 8 hours | D. 10 hours |

**Answer : **Option A

**Explanation :**

Work done by A in 1 hour = 1/4

Work done by B and C in 1 hour = 1/3

Work done by A and C in 1 hour = 1/2

Work done by A,B and C in 1 hour = 1/4+1/3 = 7/12

Work done by B in 1 hour = 7/12 â€“ 1/2 = 1/12

=> B alone can complete the work in 12 hours

| |

A. 37 Â½ days | B. 22 days |

C. 31 days | D. 22 days |

**Answer : **Option A

**Explanation :**

Work done by A in 20 days = 80/100 = 8/10 = 4/5

Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)

Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)

Work done by A and B in 1 day = 1/15 ---(2)

Work done by B in 1 day = 1/15 â€“ 1/25 = 2/75

=> B can complete the work in 75/2 days = 37 Â½ days

| |

A. 8 | B. 5 |

C. 4 | D. 6 |

**Answer : **Option D

**Explanation :**

Work done by P in 1 day = 1/18

Work done by Q in 1 day = 1/15

Work done by Q in 10 days = 10/15 = 2/3

Remaining work = 1 â€“ 2/3 = 1/3

Number of days in which P can finish the remaining work = (1/3) / (1/18) = 6

| |

A. 7 hour 15 minutes | B. 7 hour 30 minutes |

C. 8 hour 15 minutes | D. 8 hour 30 minutes |

**Answer** : Option C

**Explanation** :

Pages typed by Anil in 1 hour = 32/6 = 16/3

Pages typed by Suresh in 1 hour = 40/5 = 8

Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3

Time taken to type 110 pages when Anil and Suresh work together = 110 Ã— 3 /40 = 33/4

= 8 Â¼ hours = 8 hour 15 minutes

| |

A. 1 | B. 2 |

C. 3 | D. 4 |

**Answer :** Option D

**Explanation :**

Work done by Q in 1 day = 1/12

Work done by P in 1 day = 2 Ã— (1/12) = 1/6

Work done by P and Q in 1 day = 1/12 + 1/6 = Â¼

=> P and Q can finish the work in 4 days

| |

A. 1:3 | B. 4:3 |

C. 2:3 | D. 2:1 |

**Answer :** Option B

**Explanation :**

Work done by 20 women in 1 day = 1/16

Work done by 1 woman in 1 day = 1/(16Ã—20)

Work done by 16 men in 1 day = 1/15

Work done by 1 man in 1 day = 1/(15Ã—16)

| |

A. Rs.40 | B. Rs.70 |

C. Rs.90 | D. Rs.100 |

**Answer : **Option B

**Explanation :**

Amount Earned by P,Q and R in 1 day = 1620/9 = 180 ---(1)

Amount Earned by P and R in 1 day = 600/5 = 120 ---(2)

Amount Earned by Q and R in 1 day = 910/7 = 130 ---(3)

(2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day

- Amount Earned by P,Q and R in 1 day = 120+130-180 = 70

=>Amount Earned by R in 1 day = 70

Ratio of the capacity of a man and woman =1/(15Ã—16) : 1/(16Ã—20) = 1/15 : 1/20

= 1/3 :1/4 = 4:3

| |

A. 10 days | B. 14 days |

C. 15 days | D. 9 days |

**Answer : **Option C

**Explanation :**

Amount of work P can do in 1 day = 1/20

Amount of work Q can do in 1 day = 1/30

Amount of work R can do in 1 day = 1/60

P is working alone and every third day Q and R is helping him

Work completed in every three days = 2 Ã— (1/20) + (1/20 + 1/30 + 1/60) = 1/5

So work completed in 15 days = 5 Ã— 1/5 = 1

Ie, the work will be done in 15 days

| |

A. 18 days | B. 22 Â½ days |

C. 24 days | D. 26 days |

**Answer : **Option B

**Explanation :**

If A completes a work in 1 day, B completes the same work in 3 days

Hence, if the difference is 2 days, B can complete the work in 3 days

=> if the difference is 60 days, B can complete the work in 90 days

=> Amount of work B can do in 1 day= 1/90

Amount of work A can do in 1 day = 3 Ã— (1/90) = 1/30

Amount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45

=> A and B together can do the work in 45/2 days = 22 Â½ days

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