p,q,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:r.

Dear student

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

Regards

Arun (askIITians forum expert)