**Directions(1-5):** Find the relationship between x and y and choose a correct option.

- I.9x^2 – 94.5x + 243 = 0

II.4.5y^2 – 13.5y – 486 = 0y>=xy>xx>yx>=yNo relationship established.Option E

I.9x^2 – 94.5x + 243 = 0

=>9x^2 – (54+40.5)x + 243 = 0

=> x = 6,4.5

II.4.5y^2 – 13.5y – 486 = 0

=>4.5y^2 – 54y + 40.5y – 486 =0

=>y = 12,-9

No relation. - I. 55x^2 – 495x + 1100 = 0

II.5y^2 + 10y – 120 = 0y>xy>=xx>=yx>yNo relationship established.Option C

55x^2 – (220+275)x + 1100 = 0

=> x = 4,5

5y^2 + 30y – 20y – 120 = 0

=> y = -6,4

x>=y - I.2x^2 – x – 241 = 0

II. 2y^2 + 43y + 241 = 0No relationship established.x>yy>xx>=yy>=xOption D

2x^2 – 22x + 21x – 241 = 0

=> x = 11, -10.5

2y^2 + 21y + 22y + 241 = 0

=> y = -10.5, -11

x>=y - I.x^2 – 15x + 56 = 0

II.y^2 – 23y + 132 = 0x>yx>=yNo relationship established.y>=xy>xOption E

=>x^2 – 8x – 7x + 56 =0 => x(x-8)- 7(x-8) = 0

=>x = 7,8

y^2 – 12y – 11y +132 = 0

=>y(y-12) – 11(y-12) = 0

=>y = 11,12

y>x - I.X^2 – 22x + 120 = 0

II.y^2 – 26y + 168 = 0No relationship established.y>=xy>xx>=yx>yOption B

x^2 – 10x – 12x +20 = 0

=> x(x-10) – 12(x-10) = 0

=> x = 10,12

y^2 – 14y – 12y + 168 = 0

=> y(y-14)- 12(y-14) =0

=> y = 12,14

y>=x - The expenditure for the 7 years together forms what per cent of the revenues during the same period(approx)?
55.5%66.3%75.5%60.8%80.8%Option C

Required answer = 877/1165 =75.5% - Which year showed the greatest percentage increase in profit as compared to the previous year?
20032005200420022001Option A

To find the answer we have to find the profit in each year.

In 2001 = 5/20*100=25%

In 2002 = 5/25*100=20%

In 2003 = 10/30*100=33.33%

In 2004 = 10/40*100=25%

In 2005 = 10/50*100=20%

In 2006 = 10/60*100 = 16.66% From the above table, In 2003 the profit is maximum. - In which year was the growth in expenditure maximum as compared to the previous year?
20012000200320052004Option C

To find the answer we have to find the profit in each year.

In 2001=8/102*100=7.8%

In 2002=5/110*100=4.5%

In 2003=10/115*100=8.7%

In 2004=10/125*100=8%

In 2005=5/135*100=3.7%

In 2006=10/140*100=7.14%

From the above table, In 2003 the expenditure is maximum. - If the profit in 2007 shows the annual rate of growth as it had shown in 2006 Over the previous year, then what approximately will be the profit in 2007?
7582709166Option B

Profit in 2005 = 60.

Profit in 2006 = 70.

Growth percentage in profit in 2006 over 2005 = (10/60) x 100 = 16.66%

Profit in 2007 will be (16.66% of 70) + 70 = Rs. 82 lakh - The average revenue collected in the given 7 years is approximately.
178156112194167Option E

Average = (120 +130 +145+ 165 +185 +200 +220)/7

= 166.42 = Rs. 167 lakh

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Directions(6-10):** Study the following charts and answer the following questions.