**Time & Work**

Time and work are concerned with the amount of time it takes an individual or a group of people to perform a task, as well as the efficiency with which each of them completes it.

The following are the basic types of questions that may be asked in the exam about the time and work topic:

- To find the efficiency of a person
- To find the time taken by an individual to do a piece of work
- To find the time taken by a group of individuals to complete a piece of work
- Work done by an individual in a certain time duration
- Work done by a group of individuals in a certain time duration

**Important Time & Work formulas**

- Work Done = Time Taken × Rate of Work
- Rate of Work = 1 / Time Taken
- Time Taken = 1 / Rate of Work
- If a piece of work is done in x number of days, then the work done in one day = 1/x
- Total Wok Done = Number of Days × Efficiency
- Efficiency and Time are inversely proportional to each other

**Solved Examples**

**Q.1. A can do a piece of work in 18 days. B can do the same work in 36 days. If A & B work together. Find how much time they will take to complete the work?**

**Solution:**

A= 18 days ; B= 36 days

Total Work= 36 (Take L.C.M of 18 & 36)

Efficiency of A= 2

Efficiency of B= 1

Total work of A+B= 36/3 = 12 days

**Q.2. A can do a piece of work in 20 days. If A & B working together takes 12 days to complete the same work. Then in how many days B alone can complete the work?**

**Solution:**

A= 20 days; A+B= 12 days

Total Work= 60

Efficiency of A= 3

Efficiency of A+B= 5

A+B= 5

3+B= 5

B= 2

Total work done by B alone= 60/2= 30 days

**Q.3. A & B can do a piece of work in 10 days. B & C in 15 days. C & A in 20 days. In how many days C alone can complete the work? **

**Solution:**

Given, A+B= 10 days; B+C= 15 days; C+A= 20 days

Total work= 60

Efficiency of A+B= 6

Efficiency of B+C= 4

Efficiency of C+A= 3

2(A+B+C)= 13

A+B+C= 13/2

6+C= 13/2

C= 13/2-6

(13-12)/2= 1/2

Total work done by C alone= 60/1/2= 60*2= 120 days

**Q.4. A can complete the work in 35 days. B can complete the same work in 15 days. They work together for 8 days then B left the work. In how many days will A alone do 60% of the remaining work?**

**Solution: **

A= 35 days; B= 15 days;

Total work= 105

Efficiency of A= 3

Efficiency of B= 7

Total work done by A&B= 7+3= 10

Total work done by B in 8 days= 8*10= 80

Remaining work= 105-80= 25

A= (25* 0.6)/3= 5 days.

**Q.5. A can do 40% of work in 12 days. B can do the same work 60% of same work in 15 days. Both work together for 10 days. C can complete the remaining work in 4 days. A,B,C together will complete 28% of same work in?**

**Solution:**

A= 40% in 12 days

= 12/40* 100= 30 days.

B= 60% in 15 days

= 15/60*100= 25 days

A= 30 days; B= 25 days; Total work= 150

Efficiency of A= 5; Efficiency of B= 6

Work done by A+B in 10 days= (5+6)*10= 110

Remaining work= 150-110= 40

Efficiency of C= 40/4= 10

A+B+C= (15*0.28)/5+6+10

= (150*0.28)/ 10= 4.2

**Q.6. A,B & C can do a piece of work in 24,30 & 40 days. They worked together but C left 4 days before the completion of work. In how many days will the work be completed?**

**Solution: **

A= 24 days; B= 30 days; C= 40 days

Total work of A, B & C= 120

Efficiency- A: 5; B: 4; C: 3

Total work done by C= 3*4= 12

A+B+C= = 120+12= 132

T= 132/12= 11 days

**Q.7. Anu, Vinu & Manu can complete a work in15, 12 & 20 days. Vinu works everyday. Anu works only on alternate days starting from the first day while Manu works only on alternate days starting from second day. The number of days needed to complete the work is?**

**Solution: **

Anu= 15 days; Vinu= 12 days; Manu= 20 days

Total work done by Anu, Vinu & Manu= 60

Efficiency; Anu= 4; Vinu= 5; Manu= 3

Number of days=

Vinu+Anu= 9

Vinu+ Manu= 8

9+8 = 2 days

2*3= 6 days + 1 days= 7 days

17 units= 17*3

51 units+ 9 = 60 units

=7 days

**Q.8. B is twice as efficient A, A can do a piece of work in 15 days. A started the work & B joined him after a few days. They completed the work in 11 days. For how many days did A work alone?**

**Solution**:

**Efficiency –**

A:B= 1:2

Total work done by A= 11*1= 11

Remaining work- 15-11= 4

Total work done by B= 4/2= 2 days

A worked alone for= 11-2= 9 days.

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