# A, B, and C entered into a business and the ratio of their investments was 5 ∶ 3 ∶ 4. After 6 months B invested Rs. 1,000 more and after 8 months C in

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A, B, and C entered into a business and the ratio of their investments was 5 ∶ 3 ∶ 4. After 6 months B invested Rs. 1,000 more and after 8 months C invested Rs. 2,000 more. At the end of one year, the profit ratio was 45 ∶ 42 ∶ 56, then the investment of B at the beginning was
1. Rs. 320
2. Rs. 360
3. Rs. 240
4. Rs. 900

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Correct Answer - Option 4 : Rs. 900

Given:

A, B, and C entered into a business and the ratio of their investments was 5 ∶ 3 ∶ 4.

Calculations:

Let the ratio of initial investments be 5x, 3x, and 4x.

Ratio of their investments = 5x × 12 ∶ {3x × 6 + (3x + 1000) × 6} ∶ {4x × 8 + (4x + 2000) × 4}

⇒ 30x ∶ (18x + 3000) ∶ (24x + 4000)

According to the question,

$\Rightarrow \frac{30x}{18x\ + \ 3000}\ =\ \frac{45}{42}$

$\Rightarrow \frac{30x}{18x\ + \ 3000}\ =\ \frac{15}{14}$

⇒ 28x = 18x + 3000

⇒ 10x = 3000

⇒ x = 300

The B’s investment = 3x = 3 × 300 = Rs. 900

∴ The B's investment is Rs. 900.