P And Q Can Do A Work In 30 Days. Q And R Can Do The Same Work In 24

1.	P And Q Can Do A Work In 30 Days. Q And R Can Do The Same Work In 24 Days And R And P In 20 Days. They Started The Work Together, But Q And R Left After 10 Days. How Many Days More Will P Take To Finish The Work ?
Answer» LET work done by P in 1 day = p, Work done by Q in 1 day = q, Work done by R in 1 day = r p + q = 1/30 q + r = 1/24 r + p = 1/20 Adding all the above, 2P + 2Q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8 => p + q + r = 1/16 => Work done by P,Q and R in 1 day = 1/16 Work done by P, Q and R in 10 days = 10 × (1/16) = 10/16 = 5/8 Remaining work = 1 = 5/8 = 3/8 Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day = 1/16 – 1/24 = 1/48 Number of days P needs to work to complete the remaining work = (3/8) / (1/48) = 18 Let work done by P in 1 day = p, Work done by Q in 1 day = q, Work done by R in 1 day = r p + q = 1/30 q + r = 1/24 r + p = 1/20 Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8 => p + q + r = 1/16 => Work done by P,Q and R in 1 day = 1/16 Work done by P, Q and R in 10 days = 10 × (1/16) = 10/16 = 5/8 Remaining work = 1 = 5/8 = 3/8 Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day = 1/16 – 1/24 = 1/48 Number of days P needs to work to complete the remaining work = (3/8) / (1/48) = 18

P And Q Can Do A Work In 30 Days. Q And R Can Do The Same Work In 24 Days And R And P In 20 Days. They Started The Work Together, But Q And R Left After 10 Days. How Many Days More Will P Take To Finish The Work ?

Answer»

LET work done by P in 1 day = p,

Work done by Q in 1 day = q,

Work done by R in 1 day = r

p + q = 1/30

q + r = 1/24

r + p = 1/20

Adding all the above, 2P + 2Q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8

=> p + q + r = 1/16

=> Work done by P,Q and R in 1 day = 1/16

Work done by P, Q and R in 10 days = 10 × (1/16) = 10/16 = 5/8

Remaining work = 1 = 5/8 = 3/8

Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day

= 1/16 – 1/24 = 1/48

Number of days P needs to work to complete the remaining work = (3/8) / (1/48) = 18

Let work done by P in 1 day = p,