In the following question, two statements (i) and (ii) are given. Choose the valid statement. i. If x : y = 2 : 3, y : z = 4 : 5, then x : y : z = 8 : 12 : 15. ii. lf x, 2, 8, y are in continued proportion, then x = 1.

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Only (i) Explanation: i. L.C.M. of two values 3 and 4 is 12. x : y = (2 $\times$ 4) : (3 $\times$ 4) = 8 : 12 y : z = (4 $\times$ 3) : (5 $\times$ 3) = 12 : 15 x : y : z = 8 : 12 : 15 Therefore, statement (i) is valid. ii. If x, 2, 8, y are in continued proportion, x/2 = $\frac{2}{8}$ = 8/y From the first pair: x : 2 = 2 : 8 x/2 = $\frac{2}{8}$ x = $\frac{4}{8}$ x = $\frac{1}{2}$ Therefore, statement (ii) is invalid.

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