Correct Answer - Option 1 : Rs. 62,000
Given:
Meera invested Rs. 4,000 more than Bhanu and Rs. 6,000 more than Charu in the business.
Meera and Bhanu invested money for 9 months each while Charu invested money for 12 months.
Profits earned at the end of the year are in the ratio of 6 ∶ 5 ∶ 6.
Concepts used:
Net capital invested = Time for which capital is invested × capital invested
Calculation:
Let the capital invested by Meera be x.
⇒ Capital invested by Bhanu = x – 4,000
⇒ Capital invested by Charu = x – 6,000
⇒ Net capital invested by Meera = 9 × x = 9x
⇒ Net capital invested by Bhanu = 9 × (x – 4,000) = 9x – 36,000
⇒ Net capital invested by Charu = 12 × (x – 6,000) = 12x – 72,000
Ratio of profits of Meera, Bhanu and Charu = 9x ∶ 9x – 36,000 ∶ 12x – 72,000
⇒ 6 ∶ 5 ∶ 6 = 9x ∶ 9x – 36,000 ∶ 12x – 72,000
On comparing,
6/5 = 9x/(9x – 36,000)
⇒ 6/5 = x/(x – 4,000)
⇒ 6 × (x – 4,000) = 5 × x
⇒ x = Rs. 24,000
Capital invested by Meera = x = Rs. 24000
Capital invested by Bhanu = x – 4,000 = Rs. 20000
Capital invested by Charu = x – 6,000 = Rs. 18000
⇒ Total capital invested in one month by Meera, Bhanu and Charu = 24000 + 20000 + 18000 = Rs. 62,000
∴ Meera, Bhanu and Charu invested a total of Rs. 62,000 in a month.
