**Directions(1-5):** Compare the values of x and y and choose a correct option.

- I.x^2 – 7x + 10 = 0

II. y^2 – 9y + 20 = 0y > xx > yx >= yx=y or relation cannot be established.y >= xOption D

I.x^2 – 7x + 10 = 0

=>x^2 – 2x – 5x + 10 = 0

=> (x-2)(x-5) = 0

=> x = 2,5

II. y^2 – 9y + 20 = 0

=>y^2 -5y – 4y + 20 = 0

=> (y-5)(y-4) = 0

=> y = 5,4

x=y or relation cannot be established. - I.(x-6)^2 – x = 0

II. (y-20)^2 = 10yx >= yx=y or relation cannot be established.y > xy >= xx > yOption C

I.(x-6)^2 – x = 0

=>x^2 – 13x + 36 =0

=> x^2 -4x – 9x +36 = 0

=> (x-4)(x-9) = 0

=> x = 4, 9

II. (y-20)^2 = 10y

=>y^2 – 50y + 400 = 0

=> y^2 – 10y – 40y + 400 = 0

=>(y-10)(y-40)

= 0 => y = 10, 40

y > x - I.x^2 – 30x + 224 = 0

II. y^2 – 32y + 255 = 0y >= xx > yy > xx >= yx=y or relation cannot be established.Option E

I.x^2 – 30x + 224 = 0

=>x^2 – 14x – 16x + 224 = 0

=>(x-14)(x-16) = 0

=> x = 14,16

II. y^2 – 32y + 255 = 0

=>y^2 – 17y – 15y + 255 = 0

=> (y-17)(y-15) = 0

=> y =17, 15

x=y or relation cannot be established. - I.x^2 – 20x + 99 = 0

II. y^2 + 13y +42 = 0x=y or relation cannot be established.x >= yy >= xx > yy > xOption D

I.x^2 – 20x + 99 = 0

=>x^2 – 9x -11x + 99 = 0

=> (x-9)(x-11) = 0

=> x = 9, 11

II. y^2 + 13y +42 = 0

=>y^2 +6y+7y+42 = 0

=> (y+6)(y+7) = 0

=> y = -6,-7

x > y - I. 8x + 5y = 89

II.2x – 3y = 1x >= yx=y or relation cannot be established.x > yy > xy >= xOption C

I. 8x + 5y = 89

II.2x – 3y = 1

On solving I and II

x = 8 y = 5

x > y - A milkman mixed milk and water in an empty container in the ratio of 24:9 resp. After mixing the milkman sold 297 litres of the mixtures and then mixed 24 litres of milk in the container. After mixing 24 litres of milk, the respective ratio of the amount of milk to the amount of water in the container became 32:11. What would be the respective ratio of the amount of milk to the water, if 24 litres of water had been mixed by the milkman instead of 24 litres of milk?
72:4983:3381:4482:4588:41Option E

Let the amount of milk and water in the container be 24x and 9x resp.

Now, [24x+24]/9x = 32/11

=>x = 11

Required ratio= 264:123 = 88:41 - The total interest earned by a main in 2 years on a certain sum of money which was lent at both simple interest and compound interest in the ratio of 6:5 resp. Was Rs. 5328. The rate of simple interest was 19% while the rate of compound interest was 10%. What would be the interest , if the total amount is lent at 24% simple interest for 3 years ?
Rs.13051Rs.13070Rs.11251Rs.12672Rs.12000Option D

Let amount lent at simple interest be Rs. 6x and amount lent at compound interest be Rs. 5x.

Now, 5328 = (6x*0.19*2)+5x*{(1.1)^2 – 1}

=> x = 1600

Total amount = 11x = Rs. 17600

Required interest = (17600*0.24*3) = Rs.12672 - The cost price of an article is Rs. 24000. The shopkeeper allowed a discount of 28% on the article. If the shopkeeper would have marked the article at Rs. 800 more and would have sold the article at the same discount, then the selling price would have been increased by 20%. Find the original profit percent of the shopkeeper.
15%10%18%5%20%Option E

Let the original marked price of the article be Rs. x.

Increased marked price = Rs.(x+800)

Increased selling price = 72% of 800 = Rs. 576

Let the original selling price of the article be Rs.y 20% of y = 576

=> y = Rs. 2880

Original Profit = 2880 – 2400 = Rs. 480

Profit% = (480/2400)*100 = 20% - The curved surface area of a cylindrical vessel is 4992 cm^2. The respective ratio of the radius and the height of the vessel is 13:16. If the cylindrical vessel is full of water, then find the time taken to empty the vessel at the rate of 338 cm^3 of water per second.
192 seconds181 seconds150 seconds168 seconds177 secondsOption A

Let radius and height be 13x and 16x resp.

CSA of the cylindrical vessel 2*3*13x*16x = 4992

=> x = 2

Radius = 26 cm Height = 32 cm

Volume = 3*26*26*32 = 64896 cm^3

Required time = 64896/338 = 192 seconds - There are 24 lottery tickets in a box numbered from 1 to 24. A ticket has been drawn from the box. What will be the probability that the number on the ticket is odd number and divisible by 5?
1/151/131/121/141/11Option C

Total number of outcomes = {1 – 24}

Desired outcomes = {5,15}

Required Probability = 2/24 = 1/12

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