## Time and Work

Quantitative Reasoning

Digging a trench, painting a wall etc. are considered as work. There is a direct relation ship between work done and time.

Work Done (W) = No. Of Days (D) × No. of Men (M)

Work and men are directly proportional to each other
```⇒ W₁    M₁ × D₁
––– =  ––  –––
W₂    M₂ × D₂
```

Question 1: If 12 men do a piece of work in 80 days in how many days will 16 men do it?

(a) 30 days
(b) 40 days
(c) 50 days
(d) 60 days

Here Work done is same i.e. W₁ = W₂
```W₁    M₁ × D₁
––– = ––  –––
W₁    M₂ × D₂

12 × 80
1 = ––  –––
16 × D₂
```

D₂ = 12 ×  5 = 60 days

If A can do a piece of work in n days, then work done by A in 1 day is 1/n. Or if a person's 1 day work is 1/n, he/she finishes his/her work in n days.

Question 2: If Mohan does a work in 10 days, find his one day work.

Men and days are inversely proportional, i.e. if the number of men increases, the number of days required to complete the same work decreases and vice versa.

Work and days are directly proportional, i.e. if the work increases, the number of days required also increases, if the work is to be completed by the same number of men and vice versa.

If A is x times as good as workman B then ratio of work done by A and B is x : 1 and ratio of time taken by A and B to finish the work is 1 : x

Question 3: Radha does a piece of work in 2 days and Shyama does it in 6 days. In how many days will they do it together?

Radha's 1 day work = 1/2

Shyama finishes work in = 6 days
Shyama's 1 day work = 1/6

Together Radha's and Shyama's 1 day work = 1/2 + 1/6 = 4/6 = 2/3

Together they will finish work = 3/2 days

Question 4:  A and B together can do a job in 4 days. If A can do job in 12 days if he works alone, then how many days B alone take to complete the job?

Answer: A and B together completes jon = 4 days
A+B 1-day work = 1/4
A finishes work in = 12 days
A's 1-day work= 1/12

B's 1 day work = 1/4 - 1/12 = 2/12 = 1/6
B finishes work = 6 days

Question 5: A is thrice good as B and both takes 8 days to complete a work. Find the number of days that B alone will take to complete the work.

Answer: Let time take by B to finish work = b days
⇒ Time taken by A to finish that work = b/3 days

Let total work = w

```                      w     3w
⇒ 1-day work of A = –––  = –––
b/3     b

w
⇒ 1-day work of B = –––
b

3w    w    4w
⇒ 1-day work of A+B = ––– + ––– = –––
b     b     b

It is given A+B together finishes work = 8 days
⇒ 1-day work of A+B = 1/8

4w     1
⇒ 1-day work of A+B = –––  = –––
b      8
⇒ b = 32

```

∴  B will finish work in 32 days.