When x is added to each of 20, 34, 11 and 16, then the numbers so obtained, in this order, are in proportion. Then, if 3x : y :: y : (2x-6), and y > 0, what is the value of y?

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This question was previously asked in

RRB NTPC Graduate Level CBT-I Official Paper (Held On: 06 Jun, 2025 Shift 3)

Answer 1

Given:

The numbers 20, 34, 11, and 16 become proportional when x is added to each.

3x : y :: y : (2x - 6), where y > 0.

Formula used:

For proportional numbers: (a + x) / (b + x) = (c + x) / (d + x)

For proportion: a : b :: c : d ⇒ a/b = c/d

Calculations:

For proportional numbers:

⇒ (20 + x) / (34 + x) = (11 + x) / (16 + x)

⇒ (20 + x)(16 + x) = (34 + x)(11 + x)

⇒ 320 + 36x + x² = 374 + 45x + x²

⇒ 36x - 45x = 374 - 320

⇒ -9x = 54

⇒ x = -6

For proportion 3x : y :: y : (2x - 6):

⇒ 3x / y = y / (2x - 6)

⇒ y² = 3x(2x - 6)

Substitute x = -6:

⇒ y² = 3(-6)(2(-6) - 6)

⇒ y² = 3(-6)(-12 - 6)

⇒ y² = 3(-6)(-18)

⇒ y² = 324

⇒ y = √324 = 18 (since y > 0)

∴ The correct answer is option (1).

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