# What should be subtracted from p and added to q so that the resulting ratio becomes 1 : 5?

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What should be subtracted from p and added to q so that the resulting ratio becomes 1 : 5?
1. $\dfrac{P + Q}{3}$
2. $\dfrac{P - Q}{P + Q}$
3. $\dfrac{5P - Q}{6}$
4. $\dfrac{Q - 3P}{4}$

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Correct Answer - Option 3 : $\dfrac{5P - Q}{6}$

Calculation:

Let the number be x

$\dfrac{P \ - \ x}{Q \ + \ x } = \dfrac{1}{5}$

⇒ 5P - 5x = Q + x

⇒ 5P - Q = 6x

⇒ x = $\dfrac{5P - Q}{6}$

∴ The number is $\dfrac{5P - Q}{6}$.