# Rs. 1900 is divided between A, B and C so that A's share is $1 \frac 1 2$ times of B's and B's is $1 \frac 1 2$ times of C's. What C's share?

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Rs. 1900 is divided between A, B and C so that A's share is $1 \frac 1 2$ times of B's and B's is $1 \frac 1 2$ times of C's. What C's share?
1. Rs. 800
2. Rs. 420
3. Rs. 400
4. Rs. 900

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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.