Question

If `a/b = c/d = e/f`, Prove that each of these ratios is equal to `(a + c + e)/(b + d + f)`.

Answer 1

Let `a/b = c/d = e/f` = k then a = bk, c = dk and e = fk.
Now `(a + c + e)/(b + d +f) = (bk + dk + fk)/(b + d + f)`
= `(k(b + d + f))/((b + d + f)` = k
Hence, `a/b = c/d = e/f = (a + c + e)/(b + d + f)`.
Hence proved.