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Mathematics

What quantity must be added to each term of the ratio a : b to make it c : d ?

Ratio Proportion

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Answer

Let x be added.

∴a+xb+x=cd\therefore \dfrac{a + x}{b + x} = \dfrac{c}{d}

⇒ d(a + x) = c(b + x)

⇒ ad + dx = cb + cx

⇒ cx - dx = ad - cb

⇒ x(c - d) = ad - bc

⇒ x = ad−bcc−d\dfrac{ad - bc}{c - d}

Hence, quantity that must be added = ad−bcc−d\dfrac{ad - bc}{c - d}.

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