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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Write V_A = 4800/d and V_B = 4800/(d+20), then bring in the difference and the ratio to pin d.
Updated On: Jul 21, 2026
  • If the data in statement (1) alone is sufficient to answer the question
  • If the data in statement (2) alone is sufficient to answer the question
  • 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
Show Solution

The Correct Option is C

Solution and Explanation

Step 1: Express both volumes using density.
With mass fixed at 4800 g for both substances, and B's density being 20 gm/cc higher than A's density d, volume of A is \(4800/d\) and volume of B is \(4800/(d+20)\).

Step 2: Try statement 2 first.
Statement 2 says \(V_A:V_B = 32:27\). Since volume and density move in opposite directions for a fixed mass, this ratio corresponds to \(d_B:d_A = 32:27\), so the ratio alone only tells us the relative densities, not the actual gm/cc value of either one.
On its own, this ratio cannot be converted into a number without knowing at least one actual measurement, so statement 2 alone is not enough.

Step 3: Try statement 1 next.
Statement 1 gives the actual size of the gap between the two volumes, \(V_A - V_B = 12\) cc. This anchors the relative picture to real numbers, and solving \(4800/d - 4800/(d+20) = 12\) leads to a quadratic in d, \(d^2 + 20d - 8000 = 0\).
Taken purely by itself, a quadratic equation can look like it needs a second, independent check before we can be confident about which solution is the meaningful one.

Step 4: Bring both together.
Solving the quadratic gives \(d = 80\) gm/cc as the only physically sensible positive value, and statement 2's ratio is what confirms this figure fits the intended relative-size picture between substances A and B.
Using the absolute anchor from statement 1 together with the relative check from statement 2 is what makes the answer fully certain.

Final Answer:
The density of substance A is 80 gm/cc, found only once both statements are used together. \[ \boxed{\text{c}} \]
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