An amount of money was distributed among A, B and C in the ratio p : q : r. Consider the following statements: 1. A gets the maximum share if p is greater than (q + r). 2. C gets the minimum share if r is less than (p + q). Which of the above statements is/are correct?

The correct option is 1 only.

Step-by-Step Explanation:

Let the total amount of money to be distributed among A, B, and C be $S$.

The money is distributed among A, B, and C in the ratio $p:q:r$, where $p,q,r>0$.

The share of each individual is given by:

$\text{Share of A}=\frac{p}{p+q+r}\times S$

$\text{Share of B}=\frac{q}{p+q+r}\times S$

$\text{Share of C}=\frac{r}{p+q+r}\times S$

Now, let us analyze the given statements one by one:

Analysis of Statement 1:
Statement 1 says: "A gets the maximum share if $p>(q+r)$."

Since $q>0$ and $r>0$, the sum $q+r$ is strictly greater than both $q$ and $r$ individually (i.e., $q+r>q$ and $q+r>r$).

If $p>(q+r)$, then by transitivity:
$p>q$ and $p>r$.

Since $p$ is strictly greater than both $q$ and $r$, A's share ratio ($p$) is the largest among the three. Therefore, A gets the maximum share.
Hence, Statement 1 is correct.

Analysis of Statement 2:
Statement 2 says: "C gets the minimum share if $r<(p+q)$."

Let us test this condition with a counterexample:
Suppose $p=2$, $q=5$, and $r=3$.

Check if the condition holds: $p+\mathrm{q<mo>=</mo><mn>2</mn><mo>+</mo><mn>5</mn><mo>=</mo><mn>7</mn>}$.
Since $r=3$, we have $3<7$, so the condition $r<(p+q)$ is satisfied.

Now check the shares among A, B, and C:
A's share ratio $p=2$
B's share ratio $q=5$
C's share ratio $r=3$

Here, A gets the minimum share ($2$), not C ($3$). Thus, $r<(p+q)$ does not guarantee that C gets the minimum share.
Hence, Statement 2 is incorrect.

Conclusion:
Only Statement 1 is correct.