Profit earned = (Investment × Profit percentage) ÷ 100

Profit percentage of A in 2010 = 90%

Profit percentage of B in 2010 = 70%

Given Investment of both companies = 25 lakhs

⇒ Profit earned by A in 2010 = (25 × 90)/100 = 22.5 lakhs

⇒ Profit earned by B in 2010 = (25 × 70)/100 = 17.5 lakhs

Total profit earned by A and B in 2010 = 22.5 + 17.5 = 40 lakhs

∴ Average profit of A and B in 2010 = 40/2 = 20 lakhs

Total income = Profit earned + Total investment in the year.

Profit earned = (Investment × Profit percentage) ÷ 100

Profit percentage of A in 2007 = 45%

Profit percentage of A in 2008 = 60%

Say I is the investment of A in 2007 and 2008.

⇒ Profit earned in 2007 = (I × 45)/100 = 0.45 × I

⇒ Profit earned in 2008 = (I × 60)/100 = 0.60 × I

Given Income in 2008 = 24 lakhs ⇒ I + 0.60 × I = 24 lakhs

⇒ 1.60 × I = 24 lakhs

⇒ I = 15 lakhs.

∴ Profit earned in 2007 = 0.45 × 15 = 6.75 lakhs and profit earned in 2008 = 0.60 × 15 = 9 lakhs.

∴ Difference between profits earned = 9 – 6.75 = 2.25 lakhs

Total income = Profit earned + Total investment in the year.

Profit earned = (Investment × Profit percentage) ÷ 100

Profit percentage of B in 2004 = 55%

Profit earned by B in 2004 = (12 × 55)/100 = 6.6 lakhs

Income of B in 2004 = 6.6 + 12 = 18.6 lakhs

∴ Investment of B in 2005 = 18.6 lakhs

Profit percentage of B in 2005 = 55%

∴ Profit earned by B in 2005 = (18.6 × 55)/100 = 10.23 lakhs

Profit percentage of A in 2006 = 55%

Investment = (Profit earned/Profit percentage) × 100

∴ Investment of A in 2006 = (10.15/55) × 100 = 18.45 lakhs

Let IA is the investment in 2008 by A.

Profit percent of A in 2007 = 45% and in 2008 = 60%

Total income = Profit earned + Total investment in the year.

Profit earned = (Investment × Profit percentage) ÷ 100

Profit earned by A in 2007 = (12 × 45)/100 = 5.4 lakhs

Total income by A in 2007 = 5.4 + 12 = 17.4 lakhs

Profit earned by A in 2008 = (IA × 60)/100 = 0.60 × IA

Total income of A in 2008 = 1.60 × IA

Given both incomes are equal ⇒ 1.60 × IA = 17.4 lakhs

⇒ IA = 17.4/1.6 = 10.875 lakhs

∴ Investment by A in 2008 = Rs.10, 87, 500

Total income = Profit earned + Total investment in the year.

Profit earned = (Investment × Profit percentage) ÷ 100

Profit percentage of A in 2009 = 75%

Profit percentage of B in 2009 = 80%

Say IA and IB are investments by A and B respectively in 2009.

Given IA + IB = 27 lakhs

Also IB = 0.50 × IA

⇒ 1.5 × IA = 27 lakhs

⇒ IA = 18 lakhs and IB = 9 lakhs

∴ Profit earned by A in 2009 = (18 × 75)/100 = 13.5 lakhs

Profit earned by B in 2009 = (9 × 80)/100 = 7.2 lakhs

∴ Total profit earned by two companies in 2009 = 13.5 + 7.2 = 20.7 lakhs

Total income = Profit earned + Total investment in the year.

Investment = (Profit earned/Profit percentage) × 100

Profit percentage of A in 2005 = 70%

Profit percentage of B in 2005 = 55%

Investment of A in 2005 = PA/0.7

Investment of B in 2005 = PB/0.55 [PA and PB are profits of A and B respectively]

Given both investments are same ⇒ PA/PB = 0.7/0.55

Total income of A in 2005 = PA + PA/0.7 = PA (1 + 1/0.7)

Total income of B in 2005 = PB (1 + 1/0.55)

∴ Ratio of incomes = \(\frac{{{{\rm{P}}_{\rm{A}}}}}{{{{\rm{P}}_{\rm{B}}}}} \times \frac{{1 + \frac{1}{{0.7}}}}{{1 + \frac{1}{{0.55}}}} = \frac{{0.7}}{{0.55}} \times \left( {\frac{{1.7}}{{1.55}}} \right) \times \frac{{0.55}}{{1.7}} = \frac{{1.7}}{{1.55}}\)

∴ Ratio = 1.7: 1.55 = 34: 31

Total income = Profit earned + Total investment in the year.

Investment = (Profit earned/Profit percentage) × 100

Profit percentage of B in 2006 = 65%

⇒ Investment by B in 2006 = (812500/65) × 100 = 12, 50,000

Total income in 2006 by Company B = 8, 12,500 + 12, 50,000 = Rs.20, 62,500

Number of Computers manufactured by Company B = 15

Number of Computers manufactured by all the Companies together = 10+15+7.5+22.5+30 = 85

Required Percentage = (15/85) × 100% = (3/17) × 100% = 18% (approximately)

Number of Computers manufactured by Company D = 22.5

Number of Computers manufactured by Company E = 30

Required Percentage = (22.5/30) × 100% = (0.75 × 100)% = 75%

Number of Computers sold by Company B = 12.5

Number of Computers manufactured by Company B = 15

Required Percentage = (12.5/15) ×100 % = (0.833×100)% = 83.3%

Average number of Computers manufactured by all the Companies together = (Total number of computers manufactured by all the companies)/(Total number of companies) = (10 + 15 + 7.5 + 22.5 + 30)/5 = 85/5 = 17 lakhs

Average number of Computers sold by all the Companies together = (Total number of computers sold by all the companies)/(Total number of companies) = (7.5 + 12.5 + 5 + 17.5 + 25)/5 = 67.5/5 = 13.5 lakhs

Require Difference = (17-13.5) Lakhs = 3.5 Lakhs = 350000

Number of Computers manufactured by Companies A and C together

= (10 + 7.5) = 17.5

Number of Computers sold by Companies A and C together = (7.5 + 5) = 12.5

Required ratio = 17.5/12.5 = 7/5