Important Formulas: Time and Work | Quantitative for GMAT PDF Download

Time and Work Important Concepts

Let’s have a look at some plausible insights into the concept of Man – Work- Hour: 

• More men will do more work
• More men will do more work in less time
• More work signifies more time required to do work
• If M men can do a work in T hours, then Total effort or work = MT man hours
• If X can do a piece of work in D days, then X’s 1 day work = 1/ D
• Part of Work done by X  in t days= t/D
• If X’s 1 day’s work= 1/D, then X can finish the work in D days

Time and Work Important Formulas 

Here are some important time and work formulas for GMAT that one must know to solve questions:

• Work from Days

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

• Days from Work

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

• 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

Time and Work Relationships to Remember

Mentioned below are some important relationships related to time and work tricks that aspirants or students must know while preparing for any competitive exams. These relationships are indeed shortcuts that will help you to solve time and work questions faster and with ease.   

1. Relationship between Men and Work.
   • More men  ⇒ can do  ⇒  More work
   • Less men  ⇒  can do  ⇒  Less work
2. Relationship between Work and Time
   • More work  ⇒  takes  ⇒  More Time
   • Less work  ⇒  takes  ⇒  Less Time
3. Relationship between Men and Time
   • More men  ⇒  can do in  ⇒  Less Time
   • Less men  ⇒  can do in  ⇒  More Time

Time and Work Tricks 

Mentioned below are some of the beneficial time and work tricks

Trick 1: If M1 men can finish W1 work in D1 days and M2 men can finish W2 work in D2 days then, the relation is: M1*D1/W1 = M2*D2/W2

Trick 2: If M1 men finish W1 work in D1 days, working T1 time each day and M2 men finish W2 work in D2 days, working T2 time each day, then the relation is: M1*D1*T1/W1 = M2*D2*T2/W2

Trick 3: If A completes a piece of work in ‘x’ days, and B completes the same work in ‘y’ days, then,
Work done by A in 1 day = 1/X
Work done by B in 1 day = 1/Y
Work done by A and B in 1 day = 1/X + 1/Y
Total time taken to complete the work by A and B both = XY/(X + Y)

Trick 4: If A can do a work in ‘x’ days, B can do the same work in ‘y’ days, C can do the same work in ‘z’ days, then the total time taken by A, B and C to complete the work together = XYZ/(XY + YZ + ZX)

Trick 5:  If A alone can do a certain work in ‘x’ days and A and B together can do the same work in ‘y’ days, then B alone can do the same work in = XY/(X – Y)

Trick 6: Work of one day =Total work / Total no. of working days
Total work = (work of one day) × (total no. of working days)
Remaining work = 1 – (work done)
Work done by A = (Work done in 1 day by A) × (total no. of days worked by A)

Trick 7: If A can do a work in ‘x’ days and B can do the same work in ‘y’ days and when they started working together, B left the work ‘m’ days before completion then the total time taken to complete work is = (Y + M)X / (X+Y)

Trick 8: If A leaves the work ‘m’ days before its completion then the total time taken to complete work is = (X + M)Y / (X+Y)

Trick 9: If food is available for ‘a’ days for ‘A’ men at a certain place and after ‘b’ days. ‘B’ men join, then the remaining food will serve total men for Required time = A(a – b) / (A + B) days 

Trick 10: If A and B together can finish a certain work in ‘a’ days. They worked together for ‘b’ days and then ‘B’ (or A) left the work. A (or B) finished the rest of work in ‘d’ days, then, the total time taken by A (or B) alone to complete the work = ad / (a – b) or bd / (a – b) days