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.