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A sum of Rs. 16,380 is divided among A, B, C, and D such that the ratio of the shares of A and B is 1 ∶ 3, that B and C is 2 ∶ 5, and C and D is 2 ∶ 3. The share (in Rs.) of C is:
1. 5,400
2. 8,100
3. 6,300
4. 4,500

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Correct Answer - Option 1 : 5,400

Given:

Amount divide among A, B, C, D = Rs.16,380

A : B = 1 : 3

B : C = 2 : 5

C : D = 2 : 3

Calculation:

Step 1  

A B C D
1 3    
  2 5  
    2 3

Step 2

A B C D
1 3 3 3
2 2 5 5
2 2 2 3

Step 3

A : B : C : D = (1 × 2 × 2) : (3 × 2 × 2) : (3 × 5 × 2) : (3 × 5 × 3)

⇒ A : B : C : D = 4 : 12 : 30 : 45

Now, (4 + 12 + 30 + 45)R = 16,380

⇒ 91R = 16380

⇒ R = 180 

⇒ 30R = 180 × 30

⇒ 30R = 5400

∴ The share of C is Rs. 5400.

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