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A sum of Rs. x is divided between A, B and C such that the ratio of the shares of A and B is 3 ∶ 5, and that of B and C is 4 ∶ 7. If the difference between the shares of A and C is Rs. 2001, then the value of x is∶  
1. 5,481
2. 5,742
3. 5,655
4. 5,829

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Correct Answer - Option 4 : 5,829

Given:

The sum divided among A, B and C is Rs. x

The ratio of the share of A and B is 3 : 5

The ratio of the share of B and C is 4 : 7

And the difference between shares of A and C is Rs. 2,001.

Calculation:

Ratio of A, B and C = 3 : 5 ∷ 4 : 7

⇒ (3 × 4) : (5 × 4) : (5 × 7)

⇒ 12 : 20 : 35

Let the shares be 12x, 20x and 35x respectively.

Total shares = 67x

Share of C – Share of A = 2,001

⇒ (35/67)x – (12/67)x = 2,001

⇒ (35x – 12x)/67 = 2001

⇒ 23x = 2001 × 67

⇒ x = 5,829

∴ The value of x is 5,829.

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