Question:hard

The mass of a substance A is 4.8 kg. Another substance B of the same mass has 20 gm/cc more density than A. What is the density of substance A?

Statement 1: Volume of substance B is 12 cc less than substance A.
Statement 2: The ratio of volumes of substances A and B is 32 : 27.

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Use volume = mass/density for both statements separately; check whether each equation alone has a unique valid (positive) solution for the density of A.
Updated On: Jul 20, 2026
  • If the data in statement (1) alone is sufficient to answer the question, but the data in statement (2) alone is not sufficient.
  • If the data in statement (2) alone is sufficient to answer the question, but the data in statement (1) alone is not sufficient.
  • If the data in both the statements together are needed to answer the question.
  • If either statement (1) alone or statement (2) alone is sufficient to answer the question.
  • If the data in neither statement (1) nor statement (2) is sufficient to answer the question, and more data is needed.
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The Correct Option is D

Solution and Explanation

Work with the ratio form directly instead of a quadratic. Since both substances have the same mass, their volumes are in inverse proportion to their densities: V_A/V_B = d_B/d_A.

For statement 2, we're told V_A : V_B = 32 : 27, so d_B/d_A = 32/27. Since d_B = d_A + 20, write d_A = 27t and d_B = 32t for some scale factor t (matching the given ratio in reverse, since density is inversely tied to volume ratio). Then 32t - 27t = 20, so 5t = 20, t = 4. That gives d_A = 27 x 4 = 108 g/cc - one clean answer, so statement 2 alone works.

For statement 1, set up masses directly: mass = 4800 g for each. If d_A = d, then V_A = 4800/d and V_B = 4800/(d+20), and their difference is fixed at 12 cc. Testing structurally, this becomes a quadratic in d because the unknown appears in a denominator on both sides; solving it (d^2 + 20d - 8000 = 0) factors neatly into (d-80)(d+100) = 0. Since a physical density must be positive, we discard -100 and keep d = 80 g/cc as the only sensible root, making statement 1 alone conclusive as well.

Both routes independently converge on a definite number for the density of A (though the two numbers differ, since each statement is evaluated as an independent hypothetical), so by strict data-sufficiency logic the answer is (d): either statement alone is enough. This differs from the (c) marked in the source key; the quadratic and linear equations both check out with a unique valid root each on rechecking, so the discrepancy is noted here rather than silently resolved either way.
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