Question

if x: yis the duplicate ratio of a:b, a nd a:b is the sub-duplicate ratio of a+x:a-y, then the ratios 3x:a and x-y:y will be equal​

Answer 1

Answer:Since  x : y is duplicate ratio of (x + z) and ( y + z)

∴   x : y = (x + z)2 : (y + z)2

x(y + z)2 = y (x + z)2

On  simplifying  we get

xy2 + xz2 = yx2 + yz2

⇒ x2y – xy2 = xz2 – yz2

⇒ xy(x – y) = z2(x – y)

⇒  xy = z2         (x ≠ y)

⇒ x : z : : z : y

Hence  proved.