Time & Work (Efficiency)

Let Ramesh’s efficiency be 100 units.
Since Suresh is 50% more efficient, his efficiency = 150 units.

Time taken by Suresh =
18×100/ 150​
=18×2/ 3​
$=12$ days.

So, Suresh alone will take 12 days to complete the work

Let their efficiencies be 3x, 2x, and x.

Total efficiency = 3x+2x+x=6x

They complete the work in 15 days, so total work = 15×6x=90x

Preeti’s efficiency = x.

Time required for Preeti alone = 90x/x=60 days

Rajesh’s efficiency = 1/20​
Sunil’s efficiency = 1/30​

Total efficiency = 1/20+1/30​
LCM of 20 and 30 = 60
3/60+2/60=5/60=1/12​

Work done in 5 days = 5×1/12=5/12​

Remaining work = 1−5/12=7/12​

Rajesh alone takes 20 days for full work, so for 7/12 of work:
20×7/12=10 days.

Sonali’s efficiency = 1/ 24​
Sonali + Poonam’s efficiency = 1/16​

Poonam’s efficiency =
1/16−1/24​

Taking LCM of 16 and 24 = 48

3/48−2/48=1/48​

So, Poonam alone takes 48 days.

Total work = 6 workers × 30 days = 180 worker-days

Work done in 10 days by 6 workers = 6 × 10 = 60 worker-days
Remaining work = 180 - 60 = 120 worker-days

Now, total workers = 6 + 4 = 10.

Time required = $12$ days.

Total days = 10 (already worked) + 12 = 22 days
More days required = 22 - 10 = 12 days

Let Aarti’s efficiency be 125 units (since she is 25% more efficient than Neeta).
Neeta’s efficiency = 100 units.

Time taken by Neeta =
$=25$ days.

Total work = $8\times 24=192$ worker-days.

Now, total workers = 8 + 4 = 12.

Time required = $16$ days.

Let Ajay’s efficiency be 100 units.
Since Ravi is 60% more efficient, his efficiency = 160 units.

Time taken by Ravi =
25×100/160​
=25×5/8​
=15.6 days (closest to 15 days).

Let total workers = X.

Total work = X×20
After 5 workers leave, remaining workers = X - 5.

New work time = (X−5)×25

Since total work remains same:

X×20=(X−5)×25

Solving:
20X=25X−125
5X=125
X=30

Efficiency and time are inversely proportional.

Time ratio = inverse of efficiency ratio = 4:5.

Let the less efficient worker’s efficiency be 100 units.
The more efficient worker’s efficiency = 140 units.

Time taken = 30×100/ 140=21.43 days.

Let Meena’s efficiency = 1 unit per day.
Since Kavita is twice as efficient, her efficiency = 2 units per day.

Total efficiency = 1+2=3 units per day.
Total work = Meena’s work in 18 days = 18 units.

Time taken together = 18/3=6 days.

Total work per day = 1/10​
Rajesh’s work per day = 1/15​

Mohan’s work per day = 1/10−1/15=3/30−2/30=1/30​

Mohan alone takes 30 days.

Total work per day = 1/5​
Asha’s work per day = 1/10​
Bhavya’s work per day = 1/15​

Chitra’s work per day = 1/5−(1/10+1/15)

LCM of 10 and 15 = 30

3/30+2/30=5/30​

Chitra’s efficiency = 6/30−5/30=1/30​

So, Chitra alone takes 30 days.

Arjun’s efficiency = 1/18​
Rohit’s efficiency = 1/12​

Total efficiency = 1/18+1/12=2/36+3/36=5/36​

Total time = 36/5=6

Work per day together = 1/8​
Work per day by Priya = 1/12​

Work per day by Neha = 1/8−1/12​
LCM of 8 and 12 = 24, so

3/24−2/24=1/24​

So, Neha alone takes 24 days.

Let Vikas's efficiency be 100 units.
Aman’s efficiency = 100+25%=125     units.

Since work done = efficiency × time,
Time taken by Aman = $=16$ days.

Efficiency = 1 / Time taken

• Ramesh’s efficiency = 112\frac{1}{12}121​
• Suresh’s efficiency = 116\frac{1}{16}161​

Efficiency ratio = (1/12) : (1/16) = 16:12 = 4:3

Let B’s efficiency be 100 units.
A is 20% more efficient, so A’s efficiency = 120 units.
Efficiency ratio of A to B = 120:100 = 6:5 (Incorrect)
Since efficiency means work done per unit time, the ratio should be 5:4 (Correct).