__Work From Days:__

⇒ If A can do a piece of work in n days, work done by A in 1 day = 1⁄n

__Days From Work:__

⇒ If A does 1⁄n work in a day, A can finish the work in n days

No. of days = total work / work done in 1 day

__Ratio:__

If A is thrice as good a workman as B, then:

Ratio of work done by A and B = 3:1.

Ratio of times taken by A and B to finish a work = 1:3

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 ta ken to finish a work by A and B = 1 : 3

__Problems on Time and Work__** Example 1**: Ram can do a piece of work in 12 days while Shyam can do it in 15 days. If both work it together, what time will they take to do the work?

**Explanation**: Ram’s one day’s work = 1/12

Shyam one day’s work = 1/15

Therefore, one day work by Ram & Shyam

= 1⁄12 + 1⁄15 = 3⁄20

Hence, time taken by both to complete the work = 20⁄3 days

** Example 2**: Two pipes A and B can fill a tank in 10 hours and 15 hours respectively. Find the time taken to fill the tank when both the pipes are turned on simultaneously.

**Explanation**: Part of tank filled by Pipe A = 1⁄10

Part of tank filled by Pipe B = 1⁄15

Therefore, (A+B) together can fill the tank

= 1⁄10 + 1⁄15

= 1⁄6

Hence, (A+B) together can fill the tank in 6 Hours.

** Example 3**: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?

**Explanation**: A’s 1 hour’s work = 1⁄4

(B + C)’s 1 hour’s work = 1⁄3

(A + C)’s 1 hour’s work = 1⁄2

(A + B + C)’s 1 hour’s work = (1⁄4 + 1⁄3 ) = 7⁄12

B’s 1 hour’s work = (7⁄12 – 1⁄2 ) = 1⁄12

Therefore, B alone will take 12 hours to do the work.

Time and Work alternate days problems :-

** Example 4:** If Amit alone can complete a work in 16 days and Varun alone can do in 12 days. Starting with Amit, they work on alternate days. The total work will be completed in

**Explanation**: Amit’s 1 day work = 1/16

Varun’s 1 day work = 1/12

As they are working on alternate day’s So their 2 days work = (1/16)+(1/12)

= 7/48

[here is a small technique, Total work done will be 1, right, then multiply numerator till denominator, as 7*6 = 42, 7*7 = 49, as 7*7 is more than 48, so we will consider 7*6, means 6 pairs ]

Work done in 6 pairs = 6*(7/48) = 7/8

Remaining work = 1-7/8 = 1/8

On 13th day it will A turn, then remaining work = (1/8)-(1/16) = 1/16

On 14th day it is B turn,

1/12 work done by B in 1 day

1/16 work will be done in (12*1/16) = 3/4 day

So total days = 13 3⁄4

__ Example 5:__ 4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women working together finish it ?

a) 30 days

b) 40 days

c) 50 days

d) 60 days

**Explanation**: Let 1 man’s 1 day work = x

and 1 woman’s 1 days work = y.

Then, 4x + 6y = 1/8

and 3x+7y = 1/10

solving, we get y = 1/400 [means work done by a woman in 1 day]

10 women 1 day work = 10/400 = 1/40

Therefore, 10 women will finish the work in 40 days