Mixed Quantitative Aptitude Questions Set 74

  1. There are two alloys copper and zinc. One alloy is weighing 15gram of zinc and copper in the ratio of 2:3 by weight . If 10 gram of zinc is added then find what amount of copper has to be removed from the alloy such that the final alloy has zinc and copper in the ratio 4:1 by weight?
    7 gram
    4 gram
    10 gram
    5 gram
    9 gram
    Option D
    In first alloy , the amount of zinc = (15*2)/5 = 6 and the amount of copper = (15*3)/5 = 9
    Let the copper is to be removed be x.
    Therefore, (6+10)/(9-x) = 4/1
    => x= 5 gram


  2. In a container two gallons of a mixture of spirit and water contains 10% of water. They are added to four gallons of another mixture, containing 10% of water and half a gallon of water is then added to the whole. Find the percentage of water in the resulting mixture.
    Option B
    Total mixture = 2 + 4 + ½ = 13/2 = 6.5 gallon
    Amount of water in first mixture = (2*10)/100 = 0.2
    Amount of water in second mixture = (4*10)/100 = 0.4
    Total water = 0.2+0.4+0.5 = 1.1 gallon
    Required water = (1.1 *100)/6.5 = 17%(approx.)


  3. 4 years ago, the respective ratio between 1/2 of P’s age at that time and four times of Q’s age at that time was 5 : 12. Eight years hence 1/2 of P’s age at that time will be less than Q’s age at that time by 2 years. What is Q’s present age?
    8 yrs.
    12 yrs.
    10 yrs.
    15 yrs.
    5 yrs.
    Option C
    Let present ages of P and Q be x and y resp.
    Now, ½(x-4)/4(y-4) = 5/12
    => 3x – 10y = -28——-(1)
    Also, ½(x+8) = (y+8) -2
    => x – 2y = 4 ———(2)
    On solving (1) and (2) , we get x = 24 years and y = 10 years
    Present age of Q = 10 years


  4. The simple interest accrued on a sum of certain principal is Rs. 2000 in 5 years at the rate of 4 p.c.p.a. What would be the compound interest accrued on same principal at the same rate in two years ?
    Option B
    Principal = (2000*100)/(4*5) = Rs.10,000
    Required C.I. = 10000{(1+4/100)^2 – 1} = (104^2 – 100^2) = Rs.816


  5. Annu beats Binay by 20 m in a 100 m race and Binay beats Chandu by 20 m in a 100 m race. How much start should Annu give to Chandu in a 100 m race so that both of them reach the winning post at the same time ?
    36 m
    45 m
    50 m
    30 m
    55 m
    Option A
    Ratio of speed Annu and Binay = 10:8
    Ratio of speed Binay and Chandu = 10:8
    Annu:Binay:Chandu = 100:80:64
    Annu should give 36m heat start to Chandu.


  6. A runner runs from point X to Y at a speed of 15 km/hr. A second runner simultaneously runs from point Y to X and back at a speed of 20 km/h. If they cross each other 12 minutes after the start, after how much time will they cross each other ?
    35 mins.
    25 mins.
    32 mins.
    20 mins.
    48 mins.
    Option E
    Since,12 minutes which means the distance between them is 7 km.
    Ratio = 15:20 = 3:4
    So, they cross each other after 48minutes.


  7. There are four boxes in a truck. The weight of the first box is 300 kg and the weight of the second box is 20% higher than the weight of the third box, whose weight is 25% higher than the first box’s weight. The fourth box at 400 kg is 20% lighter than the fifth box. Find the difference in the average weight of the four heaviest boxes and the four lightest boxes.
    Option B
    Weight of the first box = 300kg
    Weight of the second box = 300*(125/100)*(120/100) = 450kg
    Weight of the third box = 300*(125/100) = 375kg
    Weight of the fourth box = 400kg
    Weight of the fifth box = 400 *(100/80) = 500kg
    Required Difference = (500+450+400+375)/4 – (300+375+400+450)/4 = 1725/4 – 1525/4 = 431.25 – 381.25
    = 50


  8. If the areas of the three adjacent faces of a cuboidal box are 35 cm square, 42 cm square and 30 cm square respectively, then find the volume of the box .
    210 cu.cm
    200 cu.cm
    150 cu.cm
    125 cu. cm
    145 cu.cm
    Option A
    lb = 35 sq. cm
    bh= 42 sq. cm
    hl = 30 sq. cm
    => lb * bh * lh = 35 * 42 * 30
    => (lbh)^2 = 35 * 42 * 30
    => lbh = 210
    Hence, volume of the box = 210 cm^3


  9. One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card ( Queen and King only)?
    Option E
    Required Probability = 8/52 = 2/13


  10. How many numbers can be formed using all the digits 6, 3, 5, 3, 6, 5, 2, 4, 3, such that odd digits occupy the odd places?
    Option C
    There are five odd places and four even places , of which 3 occurs three times and 5 occurs five timesand 6 occurs two times .
    The five odd places can be arranged = 5!/(2!*3!) = 10
    The four even places can be arranged by = 4!/(2!) = 12
    Therefore, total number of ways = 12*10 = 120


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