Question

In the following question, two statements (i) and (ii) are given. Choose the valid statement.

1. If x : y = 2 : 3, y : z = 4 : 5, then x : y : z = 8 : 12 : 15.
2. lf x, 2, 8, y are in continued proportion, then x = 1.

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Only (i)

Explanation:

i.

L.C.M. of two values 3 and 4 is 12.

x : y = (2 × 4) : (3 × 4) = 8 : 12

y : z = (4 × 3) : (5 × 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 = 2/8 = 8/y`

From the first pair:

x : 2 = 2 : 8

`x/2 = 2/8`

x = `4/8`

x = `1/2`

Therefore, statement (ii) is invalid.