Correct Answer - Option 3 : Rs. 400

**Given:**

Total amount = Rs. 1900

A's share = \(1 \frac 1 2\) times of B's

And B's share = \(1 \frac 1 2\) times of C's

**Formula used:**

If the ratio of A and B = x : y

And the ratio of B and C = p : q

Then the ratio of A, B and C = xp : yp : yq

**Calculation: **

A's share = \(1 \frac 1 2\) times of B's

⇒ A's share = 3/2 of B's share

⇒ A/B = 3/2

The ratio of A and B is 3 : 2 ----(i)

B's share = \(1 \frac 1 2\) times of C's share

⇒ B's share = 3/2 of C's share

⇒ B/C = 3/2

The ratio of B and C is 3 : 2 ----(ii)

From equation (i) and (ii), we get

The ratio of share between A, B and C = 3 × 3 : 2 × 3 : 2 × 2

⇒ 9 : 6 : 4

Let the amount of A, B and C be 9x, 6x and 4x respectively

Then, total amount = 9x + 6x + 4x

⇒ 19x

According to the question, the total amount = Rs. 1900

⇒ 19x = 1900

⇒ x = 1900/19

⇒ x = Rs. 100

Now, the share of C's = 4x

⇒ 4 × 100

⇒ Rs. 400

**∴ The share of C's is Rs. 400.**