Time and Work Concept of Efficiency :
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