Question

If Q=(p+q+r)/2 & (Q-p):(Q-q):(Q-r)=17:5:8
then p:q:r=?

Answer 1

Answer:

p: q: r = 13 :25 :22

Step-by-step explanation:

Given that

Q=(p+q+r)/2

(Q-p):(Q-q):(Q-r)=17:5:8

Lets take

$\dfrac{(Q-p)}{17}=\dfrac{(Q-q)}{5}=\dfrac{(Q-r)}{8}=K$

So we can say that

Q=17 K+ p    -------(1)

Q=5 K+ q     -------(2)

Q=8 K +r    --------(3)

Now by adding all above three equations

3 Q=30 K +p+q+r  ----(4)

Also given that

2 Q = p+q+r

So now putting the values of p+q+r in equation(4)

3 Q= 30 K + 2 Q

Q = 30 K

Now from equation(1)

Q=17 K+ p

30 K = 17 K +p

So p= 13 K

Now from equation(2)

Q=5 K+ q

30 K=5 K+ q

q = 25 K

Now from equation(3)

Q=8 K +r

30 K=8 K +r

r= 22 K

⇒ p= 13 K, q= 25 K and r = 22 K

So

p: q: r = 13 K:25 K:22 K

It means that

p: q: r = 13 :25 :22