###### Formulae

1. Work Done = Time Taken × Rate of Work

2. Rate of Work = 1 / Time Taken

3. Time Taken = 1 / Rate of Work

4. If a piece of work is done in x number of days, then the work done in one day = 1/x

5. Total Wok Done = Number of Days × Efficiency

6. Efficiency and Time are inversely proportional to each other

7. X:y is the ratio of the number of men which are required to complete a piece of work, then the ratio of the time taken by them to complete the work will be y:x

8. If x number of people can do W1 work, in D1 days, working T1 hours each day and the number of people can do W2 work, in D2 days, working T2 hours each day, then the relation between them will be

(M1 x D1 x T1)/W1 = (M2 x D2 x T2)/W2

###### Exercise : Time and Work MCQ Questions and Answers

**1. **
A and B can do a piece of work in 48 days, A and C can do it in 60 days, b and c can do it 72 days. In what time can c alone do it?

A. |

B. |

C. |

D. |

**Correct Answer : B. 85 days **

**Description :**

(A+B) 1 day work = 1/48

(B+C) 1 day work = 1/72

(A+C) 1 day work = 1/60

By adding 2(A+B+C) = 1/48 +1/72+1/60 = 37/720

(A+B+C) 1 day work = 37/1440

A 1 day work = 37/1440 – 1/72 = 17/1440 = 85 days (approximately)

**2. **
A man and a boy complete a work together in 24 days. If for the last 6 days man alone does the work then it is completed in 26 days. How long the boy will take to complete the work alone?

A. |

B. |

C. |

D. |

**Correct Answer : C. 72 days **

**Description :**

(man + boy)'s 1 day's work = 1/24

Their 20 day's work = 1/24 × 20 = 5/6

The remaining 1/6 work is done by the man in 6days

Therefore, the man alone will finish the work in 6 × 6 days = 36 days

Man's 1 day's work = 1/36

Therefore, boy's 1 day's work = 1/24 – 1/36 = 3 – 2 /72 = 1/72

Therefore, the Boy alone will finish the work in 72 days.

**3. **
If a men can do 3/5 of a work in 18 days, how many days will he take to finish 2/5 of the work ?

A. |

B. |

C. |

D. |

**Correct Answer : D. 12 days **

**Description :**

x/3/5 = y/2/5;

Hence x = 18

∴ y = 5x/3 x 2/5 = 10x18/15 = 180/15 = 12.

**4. **
A, B and C can do a piece of work individually in 8, 10 and 15 days, respectively. A and B start working but A quits after working for 2 days. After this, C joins B till the completion of work. In how

A. |

B. |

C. |

D. |

**Correct Answer : B. 53/10 days **

**Description :**

No answer description available for this question. Let us discuss.

**5. **
15 labourers complete a work in 10 days working 6 hours per day. If 18 labourers are employed on that work and the work is to be completed in 5 days then how many hours per day the work should be cont

A. |

B. |

C. |

D. |

**Correct Answer : C. 10 **

**Description :**

No answer description available for this question. Let us discuss.

**6. **
A works twice as fast as B. if both of them can together finish a piece of work in 12 days, then B alone can do it in

A. |

B. |

C. |

D. |

**Correct Answer : A. 36 days **

**Description :**

B = 2A

2A ? A/3A = 12

2A/3 = 12

A = 18 days

B = 2 ? 18 = 36 days

Therefore, B alone can finish the work in 36 days.

**7. **
Sam, Bob and Kim can do a job alone in 15 days, 10 days and 30 days respectively. Sam is helped by Bob and Kim every third day. In how many days will the job be completed?

A. |

B. |

C. |

D. |

**Correct Answer : A. 9 days **

**Description :**

The work done by the three persons in 3 days ( because Sam works only on every third day)

= 3/15 + 1/10 + 1/30 = 6 + 3 + 1/30 = 10/30

= 1/3 of the work

Therefore, the job will be completed in 3 ? 3 = 9 days.

**8. **
A and B together can finish a work in 9 days. A alone can finish the work in 12 days. In how many days will B alone finish the work?

A. |

B. |

C. |

D. |

**Correct Answer : C. 36 **

**Description :**

No answer description available for this question. Let us discuss.

**9. **
Twenty four men can do a work in 35 days. How many men are required to complete the work in 21 days?

A. |

B. |

C. |

D. |

**Correct Answer : B. 40 **

**Description :**

We have M1 D1 = M2 D2

So, 24 * 35 = M2 * 21 => M2 = 40.

**10. **
Nitin and Nirdosh together can complete a piece of work in 6 days. If Nitin alone can complete the same work in 24 days; in how many days can Nirdosh alone complete that work?

A. |

B. |

C. |

D. |

**Correct Answer : B. 8 **

**Description :**

No answer description available for this question. Let us discuss.