# Work and Time

In this chapter, we will study techniques to solve problems based on work and its completion time as well as number of persons required to finish the given work in stipulated time.

Suppose that you are a contractor and you got a contract to construct a flyover in a certain time. For this, you need to calculate the number of men required to finish the work according to their work efficiency

Time and work aptitude questions are asked in every competitive exam. Placement papers for **TCS**, **Infosys**, **Wipro**, **CTS**, **HCL**, **IBM** or **Bank exam** or **MBA exams **like **CAT**, **XAT**, **MAT**, or other exams like **GRE**, **GMAT** tests always contain one or more aptitude questions from this section of quantitative aptitude. Problems on time and work which appear in CAT exams are quite advanced and complicated - But they can be solved easily if you know the basic formulas, shortcuts and tricks.

This section will provide shortcuts, tips and tricks to solve quantitative aptitude questions on time and work. These are similar to time and distance shortcuts or ratio and proportion shortcuts. So, all you have to do is be thorough with the basics and practice as many questions as you can.

** Important Relations**

**Work and Person**Directly proportional (more work, more men and conversely more men, more work).**Time and Person**Inversely proportional (more men, less time and conversely more time, less men).**Work and Time**Directly proportional (more work, more time and conversely more time, more work).

*MIND IT !*

While solving these types of problems, the work done is always supposed to be equal to 1.

# Basic Rules Related to Work and Time

*Rule - 1: Work from Days:*

If a person can do a piece of work in *n* days (hours), then that person's 1 day's (hour's), work = *1/n*

**Rule- 2 : Days from Work:**

If a person's 1 day's (hour's) work = *1/n*, then the person will complete the work in *n* days (hours).

*Rule - 3*

If a person is *n* times efficient than second person, then work done by :

Ratio of work done by First person and Second person = *n* : 1.

Ratio of times taken by First person and second person to finish a work = 1 : *n*.

*Rule - 4*

If ratio of numbers of men required to complete a work is *m : n*, then the ratio of time taken by them will be *n : m*.

# Basic Concepts of Work and Time

Most of the aptitude questions on time and work can be solved if you know the basic correlation between time, work and man-hours which you have learnt in your high school class.

**1. Analogy between problems on time and work to time, distance and speed:**

- Speed is equivalent to rate at which work is done
- Distance travelled is equivalent to work done.
- Time to travel distance is equivalent to time to do work.

**2. Man - Work - Hour Formula:**

- More men can do more work.
- More work means more time required to do work.
- More men can do more work in less time.
*M*men can do a piece of work in*T*hours, then- Rate of work * Time = Work Done
- If
*A*can do a piece of work in*D*days, then*A's*1 day's work =*1/D*. - If
*A's*1 day's work =*1/D*, then*A*can finish the work in*D*days.

Total effort or work =

MTman hours.

Part of work done by

Afor t days =t/D.

*Fast Track Techniques !!*

*Techniques - 1*

M D H / W= ConstantWhere,

M= Number of men

D= Number of days

H= Number of hours per day

W= Amount of work

*Techniques - 2*

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, then

M1 D1 H1 / W1=M2 D2 H2 / W2

*Techniques - 3*

If *A* is x times as good a workman as *B*, then:

Ratio of work done by

AandB=x : 1Ratio of times taken by

AandBto finish a work =1 : xie;Awill take (1/x)of the time taken by^{th}Bto do the same work.

*Techniques - 4*

*A* and *B* can do a piece of work in '*x'* days and '*y'* days respectively, then working together:

- They will complete the work in
(xy/x+y)days- In one day, they will finish
(x+y/xy)part of work.^{th}

*Techniques - 5*

If *A *can do a piece of work in *'x' *days, *B* can do in *'y'* days and *C* can do in *'z' *days then,

A, B and C together can finish the same work in

(xyz/xy+yz+zx)days

*Techniques - 6*

If *A *can do a work in *'x'* days and *A* and *B *together can do the same work in '*y' *days then,

Number of days required to complete the work if

Bworks alone =(xy/x-y)days

## TIPS on cracking Aptitude Questions on Work and Time

Tip #1:Assume that the productivity of each worker is constant

1. **Question: **A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs.3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

**Solution:**

Let the total amount of work to be done be W units.

Productivity of A, Pa = W/6 units per day.

Productivity of B, Pb = W/8 units per day.

3 days x [Pa + Pb + Pc] = W **=>** **Pc = W/24 units per day**

Ratio of wages of A: B: C = Ratios of their productivities = (W/6): (W/8): (W/24) = 4: 3: 1.

**Amount to be paid to C = Rs.3200 x (1/8) = Rs.400**

2. **Question: **It takes 6 hours for pump A, used alone, to fill a tank of water. Pump B used alone takes 8 hours to fill the same tank. We want to use three pumps: A, B and another pump C to fill the tank in 2 hours. What should be the rate of pump C? How long would it take pump C, used alone, to fill the tank?

**Solution:**

Let the total capacity of the tank be C liters.

Fill rate of pump A, Fa = C/6 liters per hr

Fill rate of pump B, Fb = C/8 liters per hr

2 hrs x [Fa + Fb + Fc] = C** => Fc = 5C/24 liters per hr**

Let‘t’ be the time taken by only pump C to fill the tank.

‘t’ hrs x 5C/24 = C **=> t = 24/5 = 4.8 hrs**