UPSC Prelims 2020 · CSAT
Question 38: Basic Numeracy
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 of the following is correct?
AnswerUPSC’s answer is (a).
Volume scales with the cube of the side. If P has side s, Q has side 2s, so y = 8x. Q's mass is double, n = 2m. Then u = m/x and v = n/y = 2m/(8x) = m/(4x) = u/4. So u = 4v. Remember: doubling the side multiplies volume by 8, so doubling the mass lowers the density to a quarter.
Why each option is right or wrong
- (a) Right: v = u/4, so u = 4v.
- (b) u = 2v would need the volume to be four times, not eight times, larger.
- (c) v = u would need the mass to be eight times as large.
- (d) v = 4u reverses the relationship; Q is less dense, not more.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2020, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.