Question

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

1. If (4a + 3b) : (6a +7b) = 16 : 25 then a : b = 31 : 4.
2. If (1 + x) : (3x + 1) is the duplicate ratio of 3 : 5 then x = 8.

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Only (ii)

Explanation:

i.

`(4a + 3b)/(6a +7b) = 16/25`

⇒ 25(4a + 3b) = 16(6a +7b)

⇒ 100a + 75b = 96a + 112b

⇒ 4a = 37b

⇒ `a/b = 37/4`

⇒ a : b = 37 : 4

Therefore, statement (i) is invalid.

ii.

The duplicate ratio of 3 : 5 is

3³ : 5²

9 : 25

Set up the equation,

⇒ `(1 + x)/(3x + 1) = 9/25`

⇒ 25(1 + x) = 9(3x + 1)

⇒ 25 + 25x = 27x + 9

⇒ 25 − 9 = 27x − 25x

⇒ 16 = 2x

⇒ x = 8