# A invested Rs. 2,000 more than B and Rs. 4,000 more than C in the business. A and B invested money for 6 months each while C invested money for 8 mont

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A invested Rs. 2,000 more than B and Rs. 4,000 more than C in the business. A and B invested money for 6 months each while C invested money for 8 months. If the profits earned at the end of year are in the ratio of 9 ∶ 6 ∶ 4, find the total investment made by them in one month.

1. Rs. 12,000
2. Rs. 15,000
3. Rs. 12,500
4. Rs. 15,060

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Correct Answer - Option 1 : Rs. 12,000

Given:

A invested Rs. 2,000 more than B and Rs. 4,000 more than C in the business.

A and B invested money for 6 months each while C invested money for 8 months.

Profits earned at the end of year are in the ratio of 9 ∶ 6 ∶ 4.

Concepts used:

Net capital invested = Time for which capital is invested × capital invested

Calculation:

Let the capital invested by A be x.

⇒ Capital invested by B = x – 2,000

⇒ Capital invested by C = x – 4,000

⇒ Net capital invested by A = 6 × x = 6x

⇒ Net capital invested by B = 6 × (x – 2,000) = 6x – 12,000

⇒ Net capital invested by C = 8 × (x – 4,000) = 8x – 32,000

Ratio of profits of A, B and C = 6x ∶ 6x – 12,000 ∶ 8x – 32,000

⇒ 9 ∶ 6 ∶ 4 = 3x ∶ 3x – 6,000 ∶ 4x – 16,000

On comparing,

9/6 = 3x/(3x – 6,000)

⇒ 3/2 = x/(x – 2,000)

⇒ 3 × (x – 2,000) = 2 × x

⇒ x = Rs. 6,000

⇒ Total capital invested in one month by A, B and C = x + x – 2,000 + x – 4,000 = 3x – 6,000

⇒ (3 × 6,000) – 6,000 = Rs. 12,000

A, B and C invested total of Rs. 12,000 in a month.