Quant Test for NIACL AO Prelims Exam Set – 10

  1. A boat can cover 21 km upstream and 60 km downstream in 9 hours. The speed of the boat in still water is 4 km/hr more than the speed of the stream. Find the time taken by the boat to cover 55 km upstream and 140 km downstream.
    18 hours 10 minutes
    20 hours 40 minutes
    15 hours 20 minutes
    28 hours 20 minutes
    22 hours 30 minutes
    Option E
    Let the speed of the stream be x km/hr.
    Speed of the boat in still water = x + 4 km/hr.
    21/(x+4-x)+60/(x+4+x) = 9
    => x = 6
    Upstream speed = 4 km/hr.
    Downstream speed = 16 km/hr.
    Required time = 55/4 + 140/16 = 22
    hours 30 minutes

     

  2. Area of the circular field is equal to the area of the rectangular field. Length of the rectangular field is 9 m more than the breadth of the rectangular field. Find the perimeter of the rectangular field, if the circumference of the circular field is 132 m.
    95 m
    110 m
    80 m
    150 m
    100 m
    Option D
    Let the length of the rectangular field be x m.
    Breath = (x-9) m
    Radius = 132/2*pi = 21 m
    Area of the circular filed = 22/7*21*21 = 1386 m^2
    Area of the rectangular field = x(x-9) = 1386
    => x^2 – 9x – 1386 = 0
    => x^2 – 42x + 33x – 1386 = 0
    => x = 42, – 33
    Perimeter = 2*(42+33) = 150 m

     

  3. Puja invested Rs.10,000 in a scheme offering 20% compound interest compounded annually for three years. Rohit invested Rs.12000 in another scheme offering 25% compound interest for2 years. Find the difference between the interests earned by Puja and Rohit.
    Rs.530
    Rs.480
    Rs.510
    Rs.500
    Rs.400
    Option A
    Interest earned by Puja = 10000*{(1+0.20)^3 – 1} = Rs.7280
    Interest earned by Rohit = 12000*{(1+0.25)^2 – 1} = Rs.6750
    Required difference = 7280 – 6750 = Rs.530

     

  4. Puja invested Rs.10,000 in a scheme offering 20% compound interest compounded annually for three years. Rohit invested Rs.12000 in another scheme offering 25% compound interest for2 years. Find the difference between the interests earned by Puja and Rohit.

    40
    Either 15 or 35
    35
    50
    15
    Option B
    Interest earned by Puja = 10000*{(1+0.20)^3 – 1} = Rs.7280
    Interest earned by Rohit = 12000*{(1+0.25)^2 – 1} = Rs.6750
    Required difference = 7280 – 6750 = Rs.530

     

  5. A bag contains 50 bulbs, out of which certain number of bulbs are defective. Two bulbs are randomly drawn from the bag and the probability that a defective bulb and non-defective bulb are drawn is 3/7. Find the number of defective bulbs in the bag.
    40
    Either 15 or 35
    35
    50
    15
    Option B
    Let the number of defective bulbs be x.
    And the number of non-defective bulbs = (50-x)
    Probability that a defective and a non-defective bulb are drawn = (xC1*(50-x)C1)/50C2 = 3/7 x^2 – 50x + 525 = 0
    => x^2 -35x – 15x + 525 = 0
    => x = 35,15
    Either 15 or 35

     

  6. How many four-letters words having at-least one vowel can be formed by using the letters of the word ‘BAKESHOP’?
    1250
    1320
    1560
    1660
    1490
    Option C
    Total number of ways in which letters are selected
    = 3C1*5C3 + 3C2*5C2 + 3C3*5C1 = 30+30+5 = 65
    Four letters are arranged within the word = 4! = 24 ways
    Total number of words formed = 24*65 = 1560

     


  7. Directions(6-10):
    Find out the odd one out from the following series.

  8. 17,36,91,188,321,492
    17
    36
    91
    492
    321
    Option C
    +19*1
    +19*3
    +19*5
    +19*7
    +19*9
    93 should be in place of 91.

     

  9. 21,27,52,116,197,231
    52
    21
    27
    116
    231
    Option E
    +6^1
    +5^2
    +4^3
    +3^4
    +2^5
    229 should be in place of 231.

     

  10. 9,11,15,24,54,177
    54
    177
    9
    11
    24
    Option A
    +1!+1
    +2!+2
    +3!+3
    +4!+4
    +5!+5
    52 should be in place of 54.

     

  11. 15,14,24,63,236,1175
    14
    24
    15
    1175
    63
    Option D
    *1-1^2
    *2-2^2
    *3-3^2
    *4-4^2
    *5-5^2
    1155 should be in place of 1175.

     


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