A sum of Rs 3800 is divided among three persons A, B, and C
in the ratio 1/2 : 1/3 : 3/4 what is the share of the person C?

The correct answer is Rs. 1800.

Step-by-step Explanation:

First, let us write down the given ratio of division for the shares of A, B, and C:
Ratio of shares of A : B : C = $\frac{1}{2}:\frac{1}{3}:\frac{3}{4}$

To convert this fractional ratio into an integer ratio, we find the Least Common Multiple (LCM) of the denominators 2, 3, and 4.
The LCM of 2, 3, and 4 is 12.

Now, we multiply each term of the ratio by 12:
Ratio = $\left(\frac{1}{2}\times 12\right):\left(\frac{1}{3}\times 12\right):\left(\frac{3}{4}\times 12\right)$
Ratio = 6 : 4 : 9

So, the ratio of shares of A, B, and C is 6 : 4 : 9.
Let the share of A be 6x, the share of B be 4x, and the share of C be 9x, where x is a common multiplier.

The total sum divided is Rs. 3800. Therefore, the sum of their shares equals the total sum:
6x + 4x + 9x = 3800
19x = 3800
x = $\frac{3800}{19}$
x = 200

Now, we find the share of C, which corresponds to 9x:
Share of C = 9x
Share of C = 9 × 200 = Rs. 1800

Thus, C's share is Rs. 1800.