QUESTION

CSAT

Hard

Reasoning

Prelims 2020

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=mxu = \frac{m}{x} and v=nyv = \frac{n}{y}. Which one of the following is correct?

Select an option to attempt

Explanation

Given: Volume of P = xx; Volume of Q = yy; Mass of P = mm; Mass of Q = nn.

It is given that the mass of Q is twice the mass of P, i.e., n=2mn = 2m.

Also, each side of Q is twice that of P. Let the side of P be ‘a’ units and the side of Q be ‘2a’ units.

So, the volume of P is: x=a3x = a^3, and the volume of Q is: y=(2a)3=8a3y = (2a)^3 = 8a^3.

According to the question, u=m/x=m/a3u = m/x = m/a^3 … (1), and v=n/y=2m/8a3=m/4a3v = n/y = 2m/8a^3 = m/4a^3 … (2).

From equations (1) and (2), we get: u/v=4u/v = 4, or u=4vu = 4v.

Hence, the correct answer is option (A).

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