# Pam invested certain money in start up for 4 months. Era invested Rs. 5,000 more than that of Pam for 6 months. After 4 months, Pam withdrew Rs. 1,000

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Pam invested certain money in start up for 4 months. Era invested Rs. 5,000 more than that of Pam for 6 months. After 4 months, Pam withdrew Rs. 1,000 from his capital and also Era withdrew Rs. 1,000. Ratio of profits earned at the end of one year was 2 ∶ 3. Find the amount of money invested by Era initially.

1. Rs. 5,000
2. Rs. 16,000
3. Rs. 9,000
4. Rs. 10,000

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Correct Answer - Option 2 : Rs. 16,000

Given:

Pam invested certain money in start up for 4 months. Era invested Rs. 5,000 more than that of Pam for 6 months.

After 4 months, Pam withdrew Rs. 1,000 from his capital and also Era withdrew Rs. 1,000.

Ratio of profits earned at the end of one year was 2 ∶ 3.

Concepts used:

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

Calculation:

Let capital invested by Pam be Rs. x.

⇒ Capital invested by Era = (x + 5,000)

After 4 months, Pam withdrew Rs. 1,000 from his capital.

⇒ Net capital invested by Pam = (4 × x) + {8 × (x – 1,000)} = 12x – 8,000

⇒ Net capital invested by Era = {6 × (x + 5,000)} + {6 × (x + 5,000 - 1,000)} = 12x + 54,000

⇒ Ratio of profits of Pam and Era = 12x – 8,000 ∶ 12x + 54,000 = 3x – 2000 ∶ 3x + 13500

⇒ 2/3 = (3x – 2000)/(3x + 13500)

⇒ 2 × (3x + 13500) = 3 × (3x – 2000)

⇒ 6x + 27,000 = 9x – 6,000

⇒ x = 33,000/3 = 11000

⇒ Capital invested by Era = x + 5,000 = 11,000 + 5,000 = Rs. 16,000

Era invested Rs. 16,000 in the business initially.