Question

What quantity must be added to each term of the ratio x : y so that it may become equal to c : d ?

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Solution

Let the quantity be k. Then, ⇒ (a + k)d = (b + k)c ⇒ ad + dk = bc + ck ⇒ ad - bc = ck - dk ⇒ ad - bc = k(c - d) ∴ k =

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