Time and work solved examples based on the concept of efficiency

Time and Work

Solved examples based on the concept of efficiency

💡 Pro Tip: Many students get stuck when efficiency is given in decimals (e.g., 33.33%).

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Time and Work Concept of Efficiency :

 

Work ∝ 1/ Time:

If the work Ratio of A and B is 2:1

Then,

The time Ratio of A and B is 1:2

Efficiency is indirectly proportional to the number of days.

ED = Constant

E1D1 = E2D2 = E3D3

E = Efficiency

D = Days

Ex.1 If A is 2 times efficient than B. If they both can complete a work in 12 days. Then in how many days A alone can complete work.

Sol. Method 1:

The work efficiency of A: B is 2:1

Time efficiency of A: B is 1:2

1 day's work of A = 1/x

1 days' work of B = 1/2x

Together they work in 10 days = 1/x + 1/2x = 1/12

3x/2x²= 1/12

x=18 days

Method 2:

If A is twice efficient as B.

Thrice efficient man will do work in 12 days

3 men = 12 days

1 man = 12 * 3 = 36

A's work = 36/2 = 18 Days

B's work = 36/1 = 36 Days

Method 3:

ED = E1D1

12*3 = 2*D

D =36/2 = 18 Days

B will do work in 18 Days Ans.

Ex.2 A is 3 times more efficient than B. If A can complete his work in 20 days then how many days they both complete the work.

Sol.Method 1:

The ratio of work efficiency = 3:1

The ratio of time efficiency = 1:3

A's 1 day work = 1/x

B's 1-day work = 1/3x

1/x=1/20

A will complete work in  x=20 days

B will complete work in  = 60 days

A's 1-day work = 1/20

B's 1-day work =1/60

(A+B)'s 1 day work = 1/20+1/60 = 4/60 = 1/15

A+B will do the same work in = 15 days

Method 2:

The ratio of work efficiency = 3:1

The ratio of time efficiency = 1:3

3 Times efficient A will do work in 20 days. then B will do work in 60 Days.

A's 1-day work = 1/20

B's 1-day work =1/60

(A+B)'s 1 day work = 1/20+1/60 = 4/60 = 1/15

A+B will do the same work in = 15 days

Method 3:

E1D1 = E2D2

3*20 = 1*D

D= 60 Days

Rest is same as above Ans

Ex.3 If A is 30% more efficient than B if they both can complete the work in 52 days. Then in how many days A alone completes the work.

Sol. Method 1:

Ratio of work efficiency is 130x : 100x = 13x :10x

Time efficiency is 10x : 13x

A's 1 days work = 1/10x

B's 1 day work = 1/13x

Both can complete work in 52 days

1/10x + 1/13x = 1/52

(13x+10x)/130x² = 1/52

23x/130x² = 1/52

x = (23*52)/130

A will complete same work in = [(23*52)*10]/130 = 92 days

B will complete same work in  =[(23*52)*13]/130 = 119.6 days

Method 2:

Ratio of work efficiency is 130x : 100x = 13x :10x

Time efficiency is 10x : 13x

Together they will finish work in 23x = 52 days

x = 52 * 23

A will finish work in (52*23)/13 = 92 days

B will finish work in (52*23)/10 = 119.6 days

Method 3:

E1D1 =E2D2

A will finish the work in 23*52 = 13*D

D = (23*52)/13 = 92 days Ans

Ex.4 If A is 3 times efficient than B and takes 48 days less to do work. Then in how many days B alone can complete this work.

Sol. The ratio of work efficiency = 3x: x

Time efficiency = x : 3x

A takes 48 days less than B

3x-x = 48

2x= 48

x=24

B will take 3x = 72 days, and A will take 24 days Ans

Ex.5 A is thrice as good a workman as Band, therefore, can finish a job in 40 days less than B.working together, they can do it in.

Sol.Time taken by A to complete the work = x days

Time taken by B to complete the work = 3x days

So, 3x - x = 40

2x = 40

x = 20 and 3x = 60

(A+B)'s is 1 day's work

1/20 + 1/60 = (3+1)/60 = 1/15

A and B can complete work in 15 days

Ex.6 A and B together can do a work in 12 days. B and C together can do it in 15 days. If A's efficiency is twice that of C, then the days required for B alone to finish the work is?

Sol.(A+B)'s 1 day work = 1/12

(B+C)'s 1 day work = 1/15

Difference between 1 day's work of (A-C) = 1/12- 1/15 = 1/60

                                        A : C

Ratio of work efficiency = 2x : x

Ratio of Time efficiency = x : 2x

A's 1 day work = 1/x

B's 1 day work = 1/2x

1/x - 1/2x = 1/60

(2-1)/2x = 1/60

1/2x = 1/60

x= 30

B's 1 day work

A+B = 1/12

B = 1/12- A's 1 day work

1/12- 1/30 =1/20

B's will complete the work in 20 days

Ex.7 A can do work in 5 days less than the time taken by B to do it. If both of them together take 100/9 days, the time taken by B alone to do the same work in is?

Sol. let B can do work in x days

So, A can do work in x-5 days

1/x + 1/(x-5) = 9/100

(x-5+x)/x(x-5) = 9/100

9x² - 45x = 200x-500

9x² - 225x - 20x +500 = 0

9x(x-25) - 20(x-25) = 0

(x-25)(9x-20)=0

x=25 because x not equal to 20/9