UPSC Prelims 2020·CSAT·Quantitative Aptitude·Geometry and Mensuration

Let x,y be the volumes; m,n be the masses of two metallic cubes P and Q respectively. Each side of Q is two times that of P and mass of Q is two times that of P. Let u = m / x and V = n / y , which one or the following is correct?

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Last updated 23 May 2026, 3:31 pm IST
  1. Au = 4vCorrect
  2. Bu = 2v
  3. Cv = u
  4. Dv = 4u

Explanation

To solve this, let the side of cube P be s. Since volume is the cube of the side, the volume of P is x = s cubed. Each side of cube Q is twice that of P, so the side of Q is 2s. The volume of Q is y = (2s) cubed, which equals 8 times s cubed. Therefore, y = 8x. The mass of P is m and the mass of Q is n. The problem states that mass of Q is two times that of P, so n = 2m. Now calculate the values for u and v: u = m / x v = n / y = (2m) / (8x) = m / (4x) To find the relationship between u and v, substitute m / x with u in the equation for v: v = u / 4 This can be rewritten as: u = 4v Therefore, option A is correct.
Quantitative Aptitude: Let x,y be the volumes; m,n be the masses of two metallic cubes P and Q respectively. Each side of Q is two times that o
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