**Directions(1-5) :** Find the relation between x and y and choose the correct options.

- I. 2x² + 11x + 15 = 0

II. 4y² + 22y + 24 = 0x=y or no relation cannot be established.y>xx>=yy>=xx>yOption A

I. 2x² + 11x + 15 = 0

⇒ 2x² + 6x + 5x + 15 = 0

⇒ (x + 3) (2x + 5) = 0

⇒ x = – 3, –5/2

II. 4y² + 22y + 24 = 0

⇒ 2y² + 11y + 12 = 0

⇒ 2y² + 8y + 3y + 12 = 0

⇒ (y + 4) (2y + 3) = 0

⇒ y = –4, –3/2

No relation. - I. 5x² + 29x + 20 = 0

II. 25y² + 25y + 6 = 0y>=xx>yx>=yy>xx=y or no relation cannot be established.Option D

I. 5x² + 29 + 20 = 0

⇒ 5x² + 25x + 4x + 20 = 0

⇒ (x + 5) (5x + 4) = 0

⇒ x = –5, –4/5

II. 25y² + 25y + 6 = 0

⇒ 25y² + 15y + 10y + 6 = 0

⇒ (5y + 3) (5y + 2) = 0

⇒ y = – 3/5, –2/5

y > x - I. 2x^2 − (4 + √13) x + 2√13 = 0 II. 10y^2 − (18 + 5√13)y + 9√13 = 0
y>xx>=yx>yx=y or no relation cannot be established.y>=xOption B

I.2𝑥^2 − 4𝑥 − √13𝑥 + 2√13 = 0

=>2𝑥(𝑥 − 2) − √13(𝑥 − 2) = 0

=>𝑥 = √13/ 2 , 2

II. 10𝑦^2 − 18𝑦 − 5√13𝑦 + 9√13 = 0

=>2𝑦(5𝑦 − 9) − √13(5𝑦 − 9) = 0

=> 𝑦 = √13/2 , 9/5

𝑥 ≥ y - I. 16x² + 20x + 6 = 0

II. 10y² + 38y + 24 = 0y>=xx=y or no relation cannot be established.x>=yy>xx>yOption E

I. 16x² + 20x + 6 = 0

⇒ 8x² + 10x + 3 = 0

⇒ 8x² + 4x + 6x + 3 = 0

⇒ (2x + 1) (4x + 3) = 0

⇒ x = –1/2, –3/4

II. 10y² + 38y + 24 = 0

⇒ 5y² + 19y + 12 = 0

⇒ 5y² + 15y + 4y + 12 = 0

⇒ (y + 3) (5y + 4) = 0

y = –3, –4/5

x > y - I. 2𝑥^2 + 11𝑥 + 14 = 0

II.4𝑦^2 + 12𝑦 + 9 = 0y>=xx>yx=y or no relation cannot be established.x>=yy>xOption E

I. 2𝑥^2 + 4𝑥 + 7𝑥 + 14 = 0

=>2𝑥(𝑥 + 2) + 7(𝑥 + 2) = 0

𝑥 = −2, −3.5

II. (2𝑦 + 3)^2 = 0

𝑦 = −1.5, −1.5

x < y - E can finish a piece of work in 45 days. If E, D and B work alternatively starting from E on day 1, D on day 2 and B on day 3 then, in how many days will they complete work working alternatively.
2830342622Option C

Work efficiency ratio of E, D and B

= 15 : 20 : 25

= 3 : 4 : 5

Let, E completes 3x units in one day.

In 45 days, he completes 45 × 3x = 135x units

In every three days, [3x + 4x + 5x] units are being completed.

In 33 days, 12x × 11 units will be completed.

On 34th day the remaining 3x units will be completed by E. - If C can finish a work in 8 days, what is the average of the no. of days that A, B, C, D & E take individually to finish the work?
657910Option B

Ratio of efficiency of A, B, C, D and E = 6:5:2:4:3

Ratio of number of days taken by A, B, C, D and E to complete the work

= 1/6 ∶ 1/ 5 ∶ 1/ 2 : 1/ 4 ∶ 1/ 3

= 10 : 12 : 30 : 15 : 20

C finishes the work in 8 days. A, B, D and E complete the work individually in 8/ 3 , 16/ 5 , 4 and 16/ 3 days respectively.

The required average = (8 + 16 /5 + 8 /3 + 16/ 3 + 4 )/5

= 4.64 day == 5 days - If A, D and C can finish a piece of work in 10 days. What is the ratio of the no. of days that A takes to complete the work alone to the no. of days that D takes to complete it alone?
7:35:28:51:35:4Option D

Ratio of efficiency of A, D and C

= 3 : 2 : 1

Ratio of number of days taken by A, D and C to complete the work

= 1 /3 : 1/ 2 : 1 = 2 : 3 : 6

Required ratio = 2 : 6 = 1 : 3 - A can finish a piece of work in 48 days less than C. The number of days in which they finish the work together is what percent of the number of days that C takes to do it alone?
40%32%25%20%22%Option C

Work efficiency ratio of A and C = 3 : 1

Ratio of time taken by A and C to complete the work = 1 : 3

Time taken by A to complete the work = x days

Time taken by C to complete the work = 3x days

Now, 3x – x = 48 days

⇒ 2x = 48 days

⇒ x = 24 & 3x = 72 days

C can do it alone in 72 days (A + C)’s 1 day work

= 1 /24 + 1 /72

= (3 + 1)/ 72

= 4 /72

= 1/ 18

They together can complete the work in 18 days

Therefore, required percent = 18 /72 × 100 = 25% - E can do 6/7th of a job in 24 days. Time taken by A is what percent more or less by E?
25%50%30%15%20%Option B

Ratio of efficiency of A and E is 30 : 15 = 2 : 1

Ratio of number of days taken by A and E to complete the work

= 1/2 : 1

= 1 : 2

Required % = 1 2 × 100 = 50%

**Directions(6-10) : **Given below is a pie chart. This pie chart shows the percentage efficiency (out of 100) of different people named A, B, C, D and E.