An amount of money was distributed among A, B and C in the ratio p : q : r

Correct Option (1)

Statement 1 is correct. If the amount of money is distributed among A, B, and C in the ratio p:q:r, and the condition p > (q + r) is met, it implies that the value of p is greater than the sum of q and r. This inherently means p is greater than q and also greater than r individually. Consequently, p represents the largest proportion among the three shares, ensuring that A receives the maximum share of the distributed amount.

Incorrect Options:

Statement 2 is incorrect. The condition r < (p + q) indicates that the share allocated to C is less than the combined shares of A and B. However, this condition does not definitively establish that r is the minimum share among p, q, and r. Consider the following illustrative examples:

• If p=2, q=10, and r=5: The condition r < (p + q) becomes 5 < (2 + 10), which simplifies to 5 < 12 (a true statement). In this scenario, p=2 is the minimum share, not r=5.
• If p=5, q=6, and r=4: The condition r < (p + q) becomes 4 < (5 + 6), which simplifies to 4 < 11 (a true statement). In this particular case, r=4 is indeed the minimum share.

As demonstrated, the condition r < (p + q) does not consistently guarantee that r will be the minimum share. Therefore, Statement 2 is not universally correct.