A total profit of ₹14,500 is to be distributed amongst A, B, and C such that $A:B=16:3$ and $B:C=6:20$. The share (in ₹) of C in the profit is:

The correct option is 5,000.

Let's find the share of C in the total profit of ₹14,500 step-by-step.

We are given the ratios of the shares of A, B, and C as follows:
$A:B=16:3$
and
$B:C=6:20$

To combine these ratios into a single continuous ratio $A:B:C$, we need to make the term representing B common in both ratios.
In the first ratio, the term for B is 3, and in the second ratio, the term for B is 6.
We can multiply the terms of the first ratio $A:B=16:3$ by 2 to make the B term equal to 6:
$A:B=(16\times 2):(3\times 2)=32:6$

Now that the value representing B is identical in both ratios (which is 6), we can write the combined ratio of their shares as:
$A:B:C=32:6:20$

We can simplify this ratio by dividing each term by their greatest common divisor, which is 2:
$A:B:C=16:3:10$

Let the actual shares of A, B, and C be $16x$, $3x$, and $10x$ respectively, where $x$ is a common multiplier.
The sum of their shares equals the total profit of ₹14,500:
$16x+3x+10x=14,500$

Adding the coefficients together:
$29x=14,500$

Solving for $x$:
$x=\frac{14,500}{29}$
$x=500$

Now, we can find the share of C, which corresponds to $10x$:
$\text{Share of C}=10\times 500=5,000$

Thus, the share of C in the profit is ₹5,000.