If P, Q, R be whole numbers and P : Q : R = 2 : 3 : 4 and P² + Q² + R² = 11600, then P + Q - R =

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Question

This question was previously asked in

BSSC Group D Official Paper (Held On: 11 May, 2025)

Answer 1

Given:

P : Q : R = 2 : 3 : 4

P² + Q² + R² = 11600

Formula used:

Let P = 2k, Q = 3k, R = 4k

P² + Q² + R² = (2k)² + (3k)² + (4k)²

Calculation:

(2k)² + (3k)² + (4k)² = 11600

⇒ 4k² + 9k² + 16k² = 11600

⇒ 29k² = 11600

⇒ k² = 11600 ÷ 29

⇒ k² = 400

⇒ k = √400

⇒ k = 20

P = 2k = 2 × 20 = 40

Q = 3k = 3 × 20 = 60

R = 4k = 4 × 20 = 80

P + Q - R = 40 + 60 - 80

⇒ P + Q - R = 20

∴ The correct answer is option 1.

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