Mixed Quantitative Aptitude Questions Set 221

  1. The number of boys in a class are x and the number of girls are 4 less than the number of boys. The sum of weight of boys is 630 and the average weight of boys is 45 kg. If 2 students are selected for a exam then what will be the probability that the number of boys the numbers of girls are equal ?
    4/9
    35/69
    82/265
    36/129
    1/5
    Option B
    Total number of boys = x
    number of girls = x – 4
    the number of boys = 630/45 = 14
    the number of girls = 14 – 4 = 10
    probability = 14C1 * 10C1 / 24C2
    = 14 * 10 * 2/24 * 23 = 35/69

     

  2. Difference between CI received in first 1.5 years at 20% per annum compounded annually and CI received in last 1.5 years at same rate of interest in compounded half yearly on the same sum is rs.495, then find the sum ?
    32000
    48000
    30000
    52000
    45000
    Option E
    Let sum = 100x
    total rate of in 1st 1.5 years = 20 + 10 + 20 * 10 /100 = 32%
    CI received = 100x * 32/100 = 32x
    CI received in last 1.5 years = 100x * 1.1 * 1.1 * 1.1 – 100x = 33.1x
    difference = 33.1x – 32x = 495
    1.1x = 495
    x = 450
    sum = 100x = 100* 450 = 45000

     

  3. X and Z alone can do a piece of work in 25 days and 30 days respectively, while Y takes as half time as X and Z take together. If they start working alternatively starting by Y, followed X and Z respectively, then find in how many days work will be completed ?
    5 8/17 days
    12 9/11 days
    8 2/5 days
    6 3/5 days
    26 3/8 days
    Option B
    LCM of 25 and 30 = 150
    efficiency of X = 150/25 = 6
    efficiency of Z = 150/30 = 5
    efficiency of Y = 22
    when all three works alternatively
    3 days work = 22 + 6 + 5 == 33 work
    in total 12 days = 12/3 * 33 = 132 work
    remaining work = 150 – 132 = 18
    remaining work completed by Y = 18/22 = 9/11 day
    total days = 12 9/11 days

     

  4. A boat takes total 10 hours to cover the distance of 84 km in upstream and 84 km in downstream. If the speed of boat is increased by 12km/hr, then the new upstream speed is doubled of its usual speed. Find the time taken by boat to cover 140 km in downstream.
    5
    8
    2
    6.5
    2.5
    Option A
    Let speed of boat = x km/hr
    speed of stream = y km/hr
    downstream speed = x + y
    upstream speed = x – y
    new speed of boat = x + 12
    upstream speed = x + 12 – y
    2 (x – y ) = x + 12 – y
    x – y = 12
    upstream speed = 12
    time taken by boat to cover 84 km in upstream 84/12 = 7
    time taken by boat in downstream = 10 – 7 = 3
    downstream speed = 84/3 = 28 km
    time taken by boat to cover 140 km in downstream = 140/28 = 5 hours

     

  5. A and B started a partnership business with investment (x + 500) and (x – 1000) respectively. After 6 months a withdrew 40% of his amount. If profit received by A at the end of the year is 2800 out of the total profit rs.4800, then what is the value of ‘x’ ?
    4000
    2000
    1500
    3000
    5600
    Option D
    Investment of A = (x + 500)* 6 + ( x + 500)* .6 * 6 = 6(1.6x + 800)
    investment of B = (x – 1000) * 12
    profit of A = 2800
    profit B = 4800 – 2800 = 2000
    6( 1.6x + 800)/(x – 1000)12 = 2800/2000
    8x + 4000 = 14x – 14000
    x = 3000

     

  6. I. 2x^2 – 13x + 15 = 0
    II. y^2 – 6y + 8 = 0
    X > Y
    X < Y
    X ≤ Y
    X ≥ Y
    X = Y or no relation.
    Option E
    I. 2x^2 – 10x – 3x + 15 = 0
    2x = 10, 3
    x = 5 , 1.5
    II. y^2 – 4y – 2y + 8 = 0
    y = 4, 2

     

  7. I. x^2 – 27x + 92 = 0
    II. y^2 – 17y + 60 = 0
    X > Y
    X < Y
    X ≤ Y
    X ≥ Y
    X = Y or no relation.
    Option E
    I. x^2 – 23x – 4x + 92 = 0
    x = 23, 4
    II. y^2 – 12y – 5y + 60 = 0
    y = 12 , 5

     

  8. I. x^2 = 196
    II. y^3 = 4096
    X > Y
    X < Y
    X ≤ Y
    X ≥ Y
    X = Y or no relation.
    Option B
    I. x^2 = 196
    x = 14, -14
    II. y^3 = 4096
    y = 16

     

  9. I. 5x^2 – 7x + 2 = 0
    II. y^2 + 12y + 32 = 0
    X > Y
    X < Y
    X ≤ Y
    X ≥ Y
    X = Y or no relation.
    Option A
    I. 5x^2 – 5x – 2x + 2 = 0
    5x = 5, 2
    x = 1, .4
    II. y^2 + 8y + 4y + 32 = 0
    y = -8, -4

     

  10. I. 3x^2 – 19x + 20 = 0
    II. 4y^2 – 6y + 2 = 0
    X > Y
    X < Y
    X ≤ Y
    X ≥ Y
    X = Y or no relation.
    Option A
    I. 3x^2 – 15x – 4x + 20 = 0
    3x = 15, 4
    x = 5, 1.33
    II. 4y^2 – 4y – 2y + 2 = 0
    4y = 4, 2
    y = 1. .5

     

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