p, q and r are three positive numbers and Q = p+q+r/2. If(Q-p) : (Q-q) : (Q-r) = 2 : 5 : 7, then find the ratio of p, q and r?

Q-p/Q-q/Q-r = 2:5:7

Q-p = 2K                  ........1

Q-q = 5k                  ..........2

Q-r = 7k                 .........3

adding all these eq

3Q -(p+q+r) = 14k         ...........4

p+q+r/2 = Q              (given)

using this eq 4 becomes

Q = 14k

putting Q in 1 ,2 ,3

p = 12k , q = 9k , r = 7k

ratio = p:q:r = 12:9:7

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Approved