# Time & Work Practice Problems with Answers:

**Problem 1:**

12 men take 36 days to do a work while 12 women girls can complete the 3/4^{th} of the same work in 36 days. How many days 10 men and 8 women together can complete the same work?

**Solution: **

Total Work = 12 × 36 mds (man days).

Efficiency of 1 woman= 3/4 man i.e. 1w=3/4 m

- 4women = 3men

We have to solve 10 m + 8 w =? Days to finish the work.

- 10m + 6w [:.4w= 3m]
- 16 m= ?days
- 16 men can finish the total work of (12 × 36) in [(12 ×36)/16] days.
**27 days.**

**Note: **No need to write all these steps at the time of the exam.

**Problem 2: **

Neeraj can complete a work in 15 hours. Ashish alone can complete the same work in 10 hrs. If Neeraj works alone for 9 hours and then stops. How many hours will it take Ashish to complete the work alone?

**Solution: **

Let us assume, Total time = t hrs. And total work = 1.

Work done by Neeraj + work done by Ashish = Total Work.

=> 9/15 + (t-9)/10 = 1.

=> (18 + 3t -27)/30 =1.

=> (-9 + 3 t ) = 30.

t= 39/3 = 13 hours.

Problem 3:

Aradhya can finish a work alone in 12 days. Anusha can finish the same work in 15 days. Aradhya started work alone after working 3 days Anusha joined to do the work. How many days will they now take together to finish the remaining work?

Solution:

Let us assume total time is t hours and total work is 1.

Total work = work done by Aradhya + work done by Anusha.

- t/12 + (t-3)/15 = 1,
- 5t + 4t -12 = 60
- 9t = 72
- Total time t = 8 hours.

Time taken for the remaining work = 8-3 = 5 hours.

Problem 4:

2 men can complete a piece of work in 6 days.

2 women can complete the same piece of work in 9 days.

3 child can complete the same work in 8 days.

Then, How many men required to complete remaining work?

Sol:

Total work = L.C.M. of 6, 9, 8 i.e. 72 man days.

Part 1:

3 w + 4 c worked for 1 day.

=> 18/3 + 24/4 = 6+6=12 man days

Remaining work = 72-12 = 60 man days

Remaining work can be finished by 60/12 man i.e. 5 men.

Problem 5:

If it takes for A to dig a certain ditch 4 days whereas B can dig it in 8 days and A, Band C can together dig it in 22/7 days. How long C alone would take to dig?

Sol:

C’s 1-day work = (A+B+C)’s 1-day work – (A’s 1-day work+ B’s 1-day work)

=> 7/16 – (1/4 + 1/8)

=> (7 – 4 – 2 ) / 16

=> 1/16

Therefore, C can finish it in 16 days.

Problem 6:

P can finish a work in 12 days working 8 hours a day. Q can finish the same work in 8 days working 10 hrs. a day. If P and Q work together working 8 hours a day. In how many days they finish the work?

Sol:

Total work = LCM [(12×8), (8×10)]

=> LCM(96, 80)

=> 480

(P+Q)’s 1 day work = 480/96 + 480/80

=> 5 + 6

=> 11 days

Working 8 hours = 11/8.

Problem 7:

9 girls can complete a work in 360 days. 18 men can complete the same work alone in 72 days and 12 women can complete the work in 162 days. How many days it takes for 4men, 12 women and 10 girls to finish a work together?

Sol:

4 men + 12 women + 10 girls =? Days

=> 4[1/ (18× 72)] + 12[1/ (12× 162)] + 10[1/ (9×360)]

=> 1/324 + 1/162 +1/324

=> (1 +2+1)/324 =1 / 81.

81 days to finish the work all together.

Problem 8:

A certain number of persons can complete a work in 100 days. If there be 10 persons less. It would have taken 10 days more for the work to be completed. How many number of persons in the beginning was?

Sol:

Men | Days |

x | 100 |

x-10 | 110 |

- x × 100 = (x-10) × 110
- x / (x-10) = 110 / 100
- x/(x-10) = 11/10
- 10x = 11x – 110
- X =
**110 men**

Problem 9:

16 men and 12 children together can complete work in 26 days. 13 men can complete the same work alone in 48 days. How many days will it take to finish half of that work by 12men and 6children? (Ans: 19.5 days)