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.