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$\overset \rightharpoonup {P}$ and $\overset \rightharpoonup {Q}$ are two unlike parallel forces. When the magnitude of $\overset \rightharpoonup {P}$ is doubled, it is found that the line of action of $\overset \rightharpoonup {Q}$ is midway between the lines of action of the new and the original resultants, find the ratio of P and Q.

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