P And Q Need 8 Days To Complete A Work. Q And R Need 12 Days To Compl

1.	P And Q Need 8 Days To Complete A Work. Q And R Need 12 Days To Complete The Same Work. But P, Q And R Together Can Finish It In 6 Days. How Many Days Will Be Needed If P And R Together Do It ?
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 = 1/8 ---(1) q + r= 1/12 ---(2) p+ q+ r = 1/6 ---(3) (3) – (2) => p = 1/6 - 1/12 = 1/12 (3) – (1) => r = 1/6 – 1/8 = 1/24 p + r = 1/12 + 1/24 = 3/24 = 1/8 => P and R will FINISH the work in 8 DAYS 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 = 1/8 ---(1) q + r= 1/12 ---(2) p+ q+ r = 1/6 ---(3) (3) – (2) => p = 1/6 - 1/12 = 1/12 (3) – (1) => r = 1/6 – 1/8 = 1/24 p + r = 1/12 + 1/24 = 3/24 = 1/8 => P and R will finish the work in 8 days

P And Q Need 8 Days To Complete A Work. Q And R Need 12 Days To Complete The Same Work. But P, Q And R Together Can Finish It In 6 Days. How Many Days Will Be Needed If P And R Together Do It ?

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 = 1/8 ---(1)

q + r= 1/12 ---(2)

p+ q+ r = 1/6 ---(3)

(3) – (2) => p = 1/6 - 1/12 = 1/12

(3) – (1) => r = 1/6 – 1/8 = 1/24

p + r = 1/12 + 1/24 = 3/24 = 1/8

=> P and R will FINISH the work in 8 DAYS

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 = 1/8 ---(1)

q + r= 1/12 ---(2)

p+ q+ r = 1/6 ---(3)

(3) – (2) => p = 1/6 - 1/12 = 1/12

(3) – (1) => r = 1/6 – 1/8 = 1/24

p + r = 1/12 + 1/24 = 3/24 = 1/8

=> P and R will finish the work in 8 days

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