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Q1. 
P, Q, and R together can complete a piece of work in 8 days. P alone can complete the work in 15 days, Q alone in 30 days. In how many days can R alone complete the work? 
A. 20 

B. 30 

C. 40 

D. 50 
Let the total work to be completed = 120 units (LCM of 8, 15 & 30)
In one day, thet together can do 120/8 = 15 units
In 1 day, P alone can complete 120/15 = 8 units
In 1 day, Q alone can complete 120/30 = 4 units
In 1 day, r alone can complete 15(8+4) =3 units
To complete 120 units, they will take 120/3 = 40days
Q2. 
Raj and Rik together can complete a piece of work in 6 days and the same work can be completed by Rik alone in 10 days. In how many days can Raj alone complete the work? 
A. 15 

B. 20 

C. 25 

D. 30 
Let the total work to be completed = 30 units (LCM of 10 & 6)
They together can complete 5 units per day
Rik alone does 30/10 = 3 units
Raj does 5 3 = 2 units per day
Raj can complete the work alone in 30/2 = 15 days
Q3. 
Rajesh can complete a piece of work in 20 days, Rakesh in 30 days and Ramesh in 60 days. In how many days can they together complete the same work? 
A. 8 

B. 10 

C. 12 

D. 15 
Let the total work to be completed = 60 units (LCM of 20, 30 & 60)
In one day Rajesh can do 3 units, Rakesh 2 units, and Ramesh 1 unit.
In 1 day, they together can complete 3 + 2 +1 = 6 units
To complete 60 units, they will take 60/6 = 10 days
Q4. 
Rajesh can complete a piece of work in 20 days and the same work can be completed by Rakesh in 30 days. In how many days can they together complete the same work? 
A. 6 

B. 10 

C. 18 

D. 12 
Let the total work to be completed = 60 units (LCM of 20 & 30)
In one day Rajesh can do 3 units and Rakesh 2 units.
In 1 day, they together can complete 3 + 2 = 5 units
To complete 60 units, they will take 60/5 = 12 days
Q1. 
Suraj and Santosh can complete a job in 8 days, Santosh and Saurav in 14 ^{2}/_{5} days and Suraj and Saurav in 9 days. In how many days can Suraj, Santosh and Saurav working individually complete the entire work respectively. 
A. 12, 24, 40 

B. 12, 24, 32 

C. 12, 18, 15 

D. 12, 24, 36 
Let the total units to be completed is 72. (LCM of 8, 72/5 and 9)
In 1 day Suraj and Santosh do = 9 units
In 1 day Santosh and Saurav do = 5 units
In 1 day Suraj and Saurav do = 8 units
2 (Suraj+Santosh+Saurav)  22 units per day
(Suraj+Santosh+Saurav)  22/2 = 11 units per day
Suraj alone does = 11  5 = 6 units per day
Santosh alone does = 11  8 = 3 units per day
Saurav alone does = 11  9 = 2 units per day
To complete 72 units, they will take 72/6, 72/3, 72/2
= 12 days, 24 days and 36 days (OptionD)
Q1. 
Annie takes 5 days less than Benie to complete a piece of work. Jenie takes 4 days less than Annie to do the same work. The time taken by Jenie alone to complete the work is same as the time taken by Annie and Benie together to do the same work. How many days Jenie takes to complete the work alone. 
A. 8 

B. 10 

C. 20 

D. 6 
If Benie takes x days, Annie takes x5 days and jenie takes x9 days to do the work.
As per the question, ^{1}/_{x5 } + ^{1}/ _{x }= ^{1}/_{x9}
_{Solving the equations, we get x= 15}
_{x  9 = 6}
Q2. 
A and B can complete a job in x times the time that C would take to complete it. B and C can complete it in x times the time that A would take to complete it. A and C can complete it in x times the time taken by B to complete it. Find x. 
A. 4 

B. ^{1} / _{4} 

C. ^{1} / _{2} 

D. 2 
This is possible when the efficiency of A, B, and C are equal i.e. 1:1:1.
Hence A+B will take 1/2 the time taken by C.
B+C will take 1/2 the time taken by A.
C+A will take 1/2 the time taken by B.
x= 1/2.