A, B, and C entered into a business and the ratio of their investments

1.	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 was1. Rs. 3202. Rs. 3603. Rs. 2404. Rs. 900
Answer» 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.

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 was1. Rs. 3202. Rs. 3603. Rs. 2404. Rs. 900

Answer» 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.