₹75,400 were divided among A, B and C, such that 3 times the share of A = 9 times the share of B = 4 times the share of C. Find the share of A.

The correct option is ₹36,192.

Step 1: Understand the given relationship
Let the shares of A, B, and C be represented by $A$, $B$, and $C$ respectively.
According to the problem, the total amount divided among them is ₹75,400. So:

$A+B+C=75400$

We are also given that 3 times the share of A = 9 times the share of B = 4 times the share of C.

$3A=9B=4C=k$

Step 2: Express each person's share in terms of a constant $k$
From the equality above, we can express $A$, $B$, and $C$ in terms of $k$:

$A=\frac{k}{3}$

$B=\frac{k}{9}$

$C=\frac{k}{4}$

Step 3: Find the ratio of their shares
The ratio of their shares $A:B:C$ is:

$A:B:C=\frac{1}{3}:\frac{1}{9}:\frac{1}{4}$

To clear the fractions, find the Least Common Multiple (LCM) of the denominators 3, 9, and 4. The LCM of 3, 9, and 4 is 36.
Multiply each term of the ratio by 36:

$A:B:C=\left(\frac{36}{3}\right):\left(\frac{36}{9}\right):\left(\frac{36}{4}\right)=12:4:9$

Step 4: Calculate the total ratio parts
The sum of the ratio parts is:

$12+4+9=25$

Step 5: Find the share of A
Share of A is calculated as:

$\text{Share of A}=\frac{12}{25}\times 75400$

Divide 75,400 by 25:

$\frac{75400}{25}=3016$

Now, multiply by 12:

$\text{Share of A}=12\times 3016=36192$

Thus, the share of A is ₹36,192.