Question : If $\frac{P}{2}=\frac{Q}{5}=\frac{R}{6}$, then what is the value of $P^2:(P+Q)^2:(Q+R)^2$?
Option 1: 10 : 56 : 169
Option 2: 4 : 49 : 121
Option 3: 9 : 64 : 144
Option 4: 16 : 10 : 125
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Correct Answer: 4 : 49 : 121
Solution : Given: The expression is $\frac{P}{2}=\frac{Q}{5}=\frac{R}{6}$. Let $\frac{P}{2}=\frac{Q}{5}=\frac{R}{6}=k$. ⇒ $P=2k, Q=5k, R=6k$ The value of $P^2:(P+Q)^2:(Q+R)^2$ $=(2k)^2:(2k+5k)^2:(5k+6k)^2$ $=4k^2:(7k)^2:(11k)^2$ $=4k^2:49k^2:121k^2$ $=4:49:121$ Hence, the correct answer is 4 : 49 : 121.
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Question : If p : q : r = 2 : 5 : 3 and r : s = 6 : 5, then what is the value of p : q : r : s?
Option 1: 4 : 12 : 7 : 3
Option 2: 4 : 10 : 6 : 5
Option 3: 6 : 5 : 8 : 10
Option 4: 8 : 12 : 7 : 8
Question : If $\frac{J}{4}=\frac{K}{5}=\frac{L}{3}$, what is the value of $(L + J)^2:(J +K)^2:(K +L)^2$?
Option 1: 25 : 16 : 9
Option 2: 64 : 25 : 81
Option 3: 49 : 81 : 62
Option 4: 49 : 81 : 64
Question : If p : q is 5 : 6 and q : r is 2 : 5, then what is p : q : r?
Option 1: 15 : 6 : 5
Option 2: 5 : 6 : 5
Option 3: 5 : 6 : 15
Option 4: 5 : 2 : 6
Question : If P : Q : R = 4 : 7 : 9 and R : S = 2 : 5, then what is the value of P : S?
Option 1: 8 : 45
Option 2: 1 : 5
Option 3: 9 : 57
Option 4: 10 : 43
Question : If $p: q$ is $4: 3$ and $q: r$ is $5 : 2$. Find $p: q: r$.
Option 1: 20 : 15 : 6
Option 2: 10 : 4 : 7
Option 3: 15 : 6 : 20
Option 4: 7 : 4 : 10
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