Question
If (2P+Q): (Q+ R) = (Q-P): (Q-R) = 4:3, then what is the
value of P: Q: R?Solution
(2P + Q) : (Q + R) = 4 : 3 3 × (2P + Q) = 4 × (Q + R) 6P + 3Q = 4Q + 4R 6P - 4R = Q    ----(1) (Q - P) : (Q - R) = 4 : 3 3 × (Q - P) = 4 × (Q - R) 3Q - 3P = 4Q - 4R 4R - 3P = Q   ----(2) Equating (1) and (2), 6P - 4R = 4R - 3P 9P = 8R P : R = 8 : 9 Substituting the values in (1), 6 × 8 - 4 × 9 = 12 = Q ∴ The required ratio is P : Q : R = 8 : 12 : 9
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