Mixed Quantitative Aptitude Questions Set 104

Directions(1-5): Compare I and II by solvind them individually and choose a correct options.

1. I.x^2 – 27x + 180 = 0
   II.y^2 – 20y + 96 = 0
   x > y
   x =< y
   x= y or relation cannot be established.
   x >= y
   x < y
   Option D
   I.x^2 – 27x + 180 = 0
   => x^2 – 15x – 12x + 180 = 0
   => (x-15)(x-12) = 0
   =>x = 15,12
   II.y^2 – 20y + 96 = 0
   => y^2 – 12y – 8y + 96 = 0
   => (y-12)(y-8) = 0
   =>y = 12,8
   x >= y

    

2. I.3x+5y = 32
   II.8x – 4y = 16
   x >= y
   x =< y
   x= y or relation cannot be established.
   x < y
   x > y
   Option C
   On solving I and II, we get
   x = y = 4

    

3. I.x^2 –x – 6 = 0 II. y^2 + 7y + 12 = 0
   x < y
   x >= y
   x > y
   x =< y
   x= y or relation cannot be established.
   Option C
   I.x^2 –x – 6 = 0
   => x^2 – 3x + 2x – 6 = 0
   => (x-3)(x+2) = 0
   => x = 3,-2
   II. y^2 + 7y + 12 = 0
   => y^2 + 3y + 4y + 12 = 0
   => (y+3)(y+4) = 0
   => y = -3,-4
   x > y

    

4. I.4x^2 + 7x – 2 = 0
   II. 3y^2 – 4y + 1 = 0
   x= y or relation cannot be established.
   x > y
   x < y
   x >= y
   x =< y
   Option C
   I.4x^2 + 7x – 2 = 0
   => 4x^2 – x + 8x – 2 = 0
   => (4x-1)(x+2) = 0
   => x = ¼,-2
   II. 3y^2 – 4y + 1 = 0
   => 3y^2 – 3y –y + 1 = 0
   => (3y-1)(y-1) = 0
   => y = 1/3,1
   x < y

    

5. I.3x^2 -17x + 10 = 0
   II. y^2 – 11y + 30 = 0
   x > y
   x >= y
   x < y
   x= y or relation cannot be established.
   x =< y
   Option E
   I. 3x^2 -17x + 10 = 0
   => 3x^2 – 2x – 15x + 10 = 0
   => (3x-2)(5) = 0
   => x = 2/3,5
   II. y^2 – 11y + 30 = 0
   => y^2 – 6y – 5y + 30 = 0
   => (y-6)(y-5) = 0
   => y = 6,5
   x =< y

    

6. A and B individually can complete the work in 30 days and 50 days resp. Both of them started the work together and worked for x days and then A left the work. If the remaining work is completed by B alone and the entire work is completed in 30 days. Find the value of x.
   8
   9
   11
   10
   12
   Option E
   Total work LCM(30 and 50) = 150 units
   Number of units work done by A and B alone = 150/30 = 5 units and 150/50 = 3 units resp. (5+3)*x + 3*(30-x) = 150
   => x = 12

    

7. A,B and C together started a business with initial investments in the ratio of 5:4:9 resp. After one year, A,B and C made additional investments in the ratio of 8:11:19 resp. Find the profit share of C out of the total profit of Rs. 3846 after two years.
   Rs.2000
   Rs.1850
   Rs.1888
   Rs.1923
   Rs.1900
   Option D
   Let initial investments made by A,B and C be 5x, 4x and 9x respectively Additional investments be 8y,11y and 19y.
   Ratio of investments of A:B:C = (5x+5x+8y):(4x+4x+11y):(9x+9x+19y)
   = (10x+8y): (8x+11y): (18x+19y)
   Profit share by C = (18x+19y)/(36x+38y)*3846 = Rs.1923

    

8. A mixture of milk and water contains 40% of water. If 11 litres of water is added to the mixture the quantity of milk and water becomes same. Find the initial quantity of the mixture.
   60
   62
   55
   52
   50
   Option C
   Let the initial quantity of the mixture be x litres.
   Quantity of water in the initial mixture = 0.4x litres
   Quantity of the milk in the initial mixture = 0.6x litres
   Now, 0.6x = 0.4x + 11
   => x = 55

    

9. A bag contains balls of three different colours i.e. red, blue and green. The ratio of the number of red balls to blue balls is 9:8 and the ratio of the number of blue balls to green balls is 4:3. If the difference between the number of red balls and green balls in the bag is 6, then find the total number of balls in the bag.
   40
   46
   38
   35
   44
   Option B
   Let the number of red, blue and green balls in the bag be 9x:8x:6x resp. Total number of balls in the bag = 9x+8x+6x = 23x
   Now, 9x – 6x = 6
   => x = 2
   Total number of balls in the bag = 23*2 = 46

    

10. A man picks two cards from a pack of 52 well shuffled cards without replacement. Find the probability that both the cards are even numbered of spades.
    3/660
    5/663
    7/666
    1/663
    5/671
    Option B
    Required Probability = 5/52*4/51 = 5/663