**Time and Work** Aptitude Questions and Answers – Formulas & Tricks

**Time and Work Formula:**

- Time Taken = 1 / Rate of Work
- Work Done = Time Taken * Rate of Work
- Rate of Work = 1 / Time Taken
- If a piece of work is done in X number of days, then the work done in one day = 1/X
- Total Work Done = Number of Days * Efficiency
- Efficiency and Time are inversely proportional to each other.
- 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
- If X number of people can do W1 work, in D1 days, Working T1 hrs each day and the number of people can do W2 work, in D2 days, Working T2 hrs each day, then the relation between them will be
- (M1 * D1 * T1) / W1 = (M2 * D2 * T2) / W2

- In case of three persons taking x, y and z days respectively, They can finish the work together in xyz / (xy + yz + xz)

Time and Work Aptitude Questions and Answers With Detailed Explanation – Quantitative Aptitude

## Time and Work

Question 1 |

A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

12 days | |

15 days | |

16 days | |

18 days |

Question 1 Explanation:

**Answer: Option B**

__Explanation:__

Question 2 |

P can complete a work in 12 days working 8hrs a day. Q can complete the same work in 8days working 10hrs a day. If both P and Q work together, working 8hrs a day, in how many days can they complete the work?

60/11 | |

61/11 | |

71/11 | |

72/11 |

Question 2 Explanation:

**Answer: Option A**

__Explanation:__

P can complete the work in (12 * 8)hrs = 96hrs

Q can complete the work in (8 * 10)hrs = 80hrs

Therefore, P's 1 hrs work = 1/96 and Q's 1hrs work = 1/80

(P+Q)'s 1hrs work = ( 1/96) + (1/80) = 11/480. So both P and Q will finish the work in 480/11hrs

Therefore, No.of Days of 8hrs each = (480/11) * (1/8) = 60/11

Question 3 |

A man can repair a road in 7hrs. How many men are required to repair the road in 2hrs?

17 men | |

14 men | |

13 men | |

16 men |

Question 3 Explanation:

**Answer: Option B**

__Explanation:__

M * T / W = Comstant

Where, M = Men

T = Time Taken

W = Work Load

So, here we apply

M1 * T1 / W1 = M2 * T2 / W2

Given, M1 = 4men, T1 = 7hrs , T2 = 2hrs, We have to find M2 = ?

Note, that here, W1 = W2 = 1 road, ie. equal work load

Clearly, Substituting in the above equation we get, M2 = 14 men.

Question 4 |

4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

35 | |

40 | |

45 | |

50 |

Question 4 Explanation:

**Answer: Option B**

__Explanation:__

Let 1 man's 1 day's work = x and 1 women's 1 day's work = y

Then 4x + 6y = (1/8) and 3x + 7y =(1/10)

Solving the two equation, We get x= (11/400), y = (1/400)

Therefore, 1 women's 1 day's work = (1/400)

10 women's 1 day's work = (1/400) * 10 = (1/40)

Hence, 10 women will complete the work in 40 days.

Question 5 |

Dev Completed the school project in 20days. How many days will Arun take to complete the same work if he is 25% more efficient then dev?

10 days | |

12 days | |

16 days | |

15 days |

Question 5 Explanation:

**Answer: Option C**

__Explanation:__

Let the days taken by Arun to complete the work be x

The ratio of time taken by Arun and Dev = 125:100 = 5:4

5:4 ::20:x

x = (( 4 * 20 ) / 5)

**x = 16**

Question 6 |

A can fabricate a divider in 30 days, while B alone can assemble it in 40 days, if they construct it together and get an installment of Rs. 7000, What B's offer?

2000 | |

3000 | |

4000 | |

6500 |

Question 6 Explanation:

**Answer: Option B**

__Explanation:__

A's 1 days work = 1/30,

B's 1 day work = 1/40,

Proportion of their shares = (1/30) : (1/40) = 4 : 3

B's offer = (7000 * (3/7)) =Rs. 3000

Question 7 |

A works twice as fast as B. If B can complete a work in 18 days independently, the number of days in which A and B can together finish the work is:

4 days | |

6 days | |

8 days | |

10 days |

Question 7 Explanation:

**Answer: Option B**

__Explanation:__

Ratio of rates of working of A and B = 2 : 1.

So, ratio of times taken = 1 : 2

Therefore, A's 1 day's work = 1/9

B's 1 day's work = 1/8

(A+B)'s 1 day's work = (1/9) + (1/8) = (1/6)

So, A and B together can finish the work in 6 days

Question 8 |

A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:

4 days | |

6 days | |

8 days | |

12 days |

Question 8 Explanation:

**Answer: Option B**

__Explanation:__

Suppose A, B and C take x, (x/2), and (x/3) days respectively to finish the work.

Then, ((1/x) + ( 2/x) + (3/x)) = 1/2

=> (6/x) = (1/2)

=> x = 12

So, B takes (12/2) = 6 days to finish the work.

Question 9 |

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, They completed the work in 3 days. How much is to be paid to C?

Rs. 375 | |

Rs. 400 | |

Rs. 600 | |

Rs. 800 |

Question 9 Explanation:

**Answer: Option B**

__Explanation:__

Question 10 |

The rates of working of A and B are in the proportion 3:4. The No. Of days taken by them to complete the work is in the proportion.

3 : 4 | |

9 : 16 | |

4 : 3 | |

2 : 4 |

Question 10 Explanation:

**Answer: Option C**

__Explanation:__

Ratio of time taken = (1/3 : 1/4) = 4 :3

There are 10 questions to complete.