1. If A can do a piece of work in n days, then A’s 1 day work = 1/n

2. If A’s 1 day work = 1/n then A can finish the work in n days.

3. Ratio:

If A is thrice as good 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

4. 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.

5. 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

**Exercise:**

**1.Worker A completes a Job in 10 Hours and worker B completes the same job in 12 hours .How long A and B will take to do the same Job working together?**

**Ans: **

A’s 1 hour’s work =1/10 and B’s 1 hour’s work = 1/12

(A+B)’s 1 hour’s work = (1/10+1/12)

- (A+B)’s 1 hour’s work= 11/60

Hence, both A and B will complete the job in **60/11 hours.**

**2.Ram completes a Job in 15 days and Shyam completes the same job in 20 days .How long Ram and Shyam will take to do the same Job working on alternate Day starting with Ram?**

**Ans: **

Ram’s 1 day’s work =1/15 and Shyam’s 1 day’s work = 1/20

According to Question,

Ram will work on first day then Shyam will work on second day and so on.

Therefore,

(Ram+Shyam)’s 2 day’s work= (1/15+1/20)

- (Ram+Shyam)’s 2 day’s work = 7/60

i.e total work is 60 and (Ram+Shyam) completes 7 parts of work in 2 days.

Hence, (7*8)=56 will be completed in 16 days and remaining (60-56)= 4 will be done by Ram in 4/15 days.

So, Total work will be completed in **(16+4/15)days.**

**3.A and B are two workers .A can complete a work in 20 days but with the help of B , A completes the same work in 10 days. Then calculate how long B alone will take to complete the same work? **

**Ans:**

A’s 1 day work =1/20 and( A+B)’s 1 day work = 1/10,

Therefore, B’s 1 day work = {(1/10)-(1/20)}

- B’s 1 day work=1/20

Hence, B will talk **20 days** to complete the same work.

**4.A is twice efficient as B. Both working together finish a work in 15 days. Then how long A will take to complete the same work?**

**Ans:**

As per question, A is twice efficient as B then

- A’s 1 day work : B’s 1 day work =2:1

Also, (A+B)’s 1 day work = 1/15

Dividing 1/15 in 2:1

**5. A can complete a work in 60 days and he work for 10 days and leave then B alone finishes the work in 40 days. How long B working alone will finish the whole work.**

**Ans:**