Population of State U = 75 lakh

Population of state V = 75 ×100/80

=375/4 lakh

Population of state S = 75 × 100/120

= 125/2 lakh

Population of State R = 125/2 ×100/125 = 50lakh

Population of State Q = 375/4 × 60/100

=225/4 Lakh

Population of state P = 75 × 80/100 = 60 lakh

Population of State T = 60×100/150 = 40 lakh

Let the population of state P = x lakh

∴ 125/100x = 60

x= 60 × 100/125

=48 lakhs

Required Percentage = (50/375/4 × 100)%

=53⅓%

Population of State U = 75 lakh

Population of state V = 75 ×100/80

=375/4 lakh

Population of state S = 75 × 100/120

= 125/2 lakh

Population of State R = 125/2 ×100/125 = 50lakh

Population of State Q = 375/4 × 60/100

=225/4 Lakh

Population of state P = 75 × 80/100 = 60 lakh

Population of State T = 60×100/150 = 40 lakh

Required difference = 375/4-60

                              =33.75 lakhs

Population of State U = 75 lakh

Population of state V = 75 ×100/80

=375/4 lakh

Population of state S = 75 × 100/120

= 125/2 lakh

Population of State R = 125/2 ×100/125 = 50lakh

Population of State Q = 375/4 × 60/100

=225/4 Lakh

Population of state P = 75 × 80/100 = 60 lakh

Population of State T = 60×100/150 = 40 lakh

Total Population = 225/4 + 125/2

= 118.75 lakhs

Population of State U = 75 lakh

Population of state V = 75 ×100/80

=375/4 lakh

Population of state S = 75 × 100/120

= 125/2 lakh

Population of State R = 125/2 ×100/125 = 50lakh

Population of State Q = 375/4 × 60/100

=225/4 Lakh

Population of state P = 75 × 80/100 = 60 lakh

Population of State T = 60×100/150 = 40 lakh

Required ratio = 225/4 : 125/2

 = 9:10

Probability of being a green shirt = 6/20 = 3/10

Probability of shirt not being green = 1-3/10 = 7/10

Required Probability ⁶C₁/²⁰C₁ × ⁸C₁/¹⁹C₁

_{= 6/20 × 8/19}

_=12/95

Atmost one shirt is red means either 0 or 1 shirt is red.

∴ Required probability

= (⁶C₀ × ¹⁴C₂)+(⁶C₁×¹⁴C₁)/²⁰C₂

=91+(6×14)/190

=91+84/190

=35/38

It is cleared from graph , the maximum profit was earned by company A from 2008 to 2009

In 2009, Profit earned by Company A = INR 130Crores

In 2008, Profit earned by Company A = INR 90Crores

∴ increased Percentage                       = (130-90/90×100)%

                                                          = 44.4% 

Profit earned by company A in 2011 = INR 115Crores

Profit earned by company C in 2012 = INR 115Crores

Profit earned by company A in 2007 = INR 80Crores

∴ Required Percentage = (115+115/80 ×100)%

                                   =287.5%

                                   =288% 

Profit earned by company C in 2007= INR 85 crores

Profit earned by company C in 2011 = INR 120 crores

∴ Increased Percentage = (120-85/85 ×100)%

                                    = 41.1%

                                    =40%

Profit earned by all the three companies (in INR crores)

In 2008 = 90+110+120= 320

In 2009 = 130+120+110= 360

In 2010 = 100+140+120= 360

In 2011 = 115+105+120= 340

In 2012 = 125+135+115 = 375

It is cleared from above, the maximum profit was earned by all three companies in 2012.

Profit earned by three companies in 2007

= 80+90+85

=255 crores

Profit earned by three companies in 2011

= 115+105+120

=340 crores

∴ Required ratio = 255 : 340 = 3:4

Profit earned by company B ina ll the years (INR in crores0 = 90+110+120+140+105+135 = 700

∴ Average Profit = 700/6

                         = INR 120Crores

Total production of all the grains together by Uttar Pradesh = 280+220+150+130 = 780

Now, food grains (in thousand tonnes) sold by Uttar Pradesh = 85/100 ×780

                                                                                             =663

Total producttion of wheat by Chhattisgarh, kerala and West Bengal in 2007=360+120+100=580

Total production of wheat by three states in 2008 = 101.8/100 × 580

                                                                            = 590.44

                                                                             = 590

Total production of rice by Rajasthan, Chhattisgarh and Tamil Nadu = 160+250+290= 700

Total production of jowar by Rajasthan, Chhattisgarh and Tamil Nadu = 120+210+240= 570

∴ Required difference = 700-570

                                 = 130

Total production of bajra by Rajasthan, Uttar Pradesh and Chhattisgarh = 80+130+180=390

Total production of jowar by Rajasthan, Uttar Pradesh and Chhattisgarh= 120+150+210=480

∴ Required ratio = 390 : 480

                           = 13:16

Total production of rice by Kerala and Tamil Nadu = 230+290 = 520

Total production of jowar by Kerala and Tamil Nadu =100+240 = 340

∴ Required Percentage = (520/340 ×100)

                                    = 152.9

                                    = 153%

Total production of bajra (in thousand tonnes) by all the given states in 2007

= 80+180+130+270+140+160

=960

∴ Average production = 960/6

                                  = 160

Total number of employees who joined company C in 2003 and 2004= 143+165 = 308

Total number of employees who left company E in 2003,2004 and 2005 together

= 79+82+91

=252

∴ Required ratio = 308 : 252

= 11:9

Number of employees who joined company D during all the years

= 116+208+169+142+155

= 790

∴ Required average = 790/5

  = 158

Number of employees in company A at the end of 2002 = 161+(148-58) =251

Number of employees in company B at the end of 2002 = 148+(172-60) =260

Number of employees in company C at the end of 2002 = 179+(161-90) = 250

Number of employees in company D at the end of 2002 = 116+(208-60) = 264

Number of employees in company E at the end of 2002 = 128+(191-50) = 269

Number of employees in company E at the end 2002

= 128+(191-50) = 269

Number of employees in company C at the end of 2002

= 179+(161-90) =250

Increased Percentage = (269-250/250 ×100)%

=(19/250 ×100)%

=7⅗%

Total number of employees in company A at the end of 2004

= 161+(148-58)+(135-69)+(112-88)

= 161+90+66+24

= 341

Total number of employees in company B at the end of 2003 = 148 + (172-60)+(188-96) =352

∴ Number of female employees = 352 × 6/11 = 192

From the statement II, Marked price = INR 1105/-

Discount = 20%

∴ Selling Price =80/100 ×1105

= INR 884/-

Profit gained = 4%

∴ Cost Price = 884 × 100/104

= INR 850/-

From Statement II

Let the numbers be 8x and 8y

We know that H.C.F. × L.C.M = Product of two numbers

8 × 504 = 8x ×8y

8×8×63 = 8x ×8y

64 × 63 = 8x ×8y

Comparing the values, we get the numbers 63 and 64.

From Statement II

Let the length of a rectangle be l and beadth be b.

It is given that,

l –b =6

    and 2(l+b) = 32

    l +b=16

Solving both the equations we get,

    l=11

    b=5

The length of the diagonal of the rectangle

=√l²+b²= √(11)²+(5)²

=√146