Mixed Quantitative Aptitude Questions Set 10

  1. A bag contains 50 paise, Re 1 and Rs 2 coins in the ratio 8 : 5 : 3 respectively. If the total value of money in bag is Rs 150, what is the total number of coins in the bag?
    A) 165
    B) 175
    C) 150
    D) 170
    E) None of these
    View Answer
     Option E
    Solution:

    Coins – 8x, 5x, 3x, so
    Value of 50 paise coins = (50/100)*8x = 4x, of Re 1 coins = 1*5x = 5x, and of Rs 2 coins = 2*3x = 6x
    So total value is 4x + 5x + 6x = 15x which equals 150, so x = 10
    Total coins = 8x + 5x + 3x = 16x = 160
  2. A boat takes 20 minutes more to travel 10 km upstream than to travel same distance downstream. If the speed of stream is 4 km/hr, find the downstream speed.
    A) 16 km/hr
    B) 18 km/hr
    C) 20 km/hr
    D) 24 km/hr
    E) 25 km/hr
    View Answer
     Option C
    Solution:

    Let speed of boat in still water = x km/hr
    So speed upstream = x-4, and speed downstream = x+4
    Now given:
    Time to travel 10 km downstream + 20/60= time to travel 10 km upstream
    So 10/(x+4) + 1/3 = 10/(x-4)
    10/(x-4) – 10/(x+4) = 1/3
    10x+40 – (10x-40)/(x<sup>2</sup> – 16) = 1/3
    80/(x<sup>2</sup> – 16) = 1/3
    x<sup>2</sup> – 16 = 240
    solve, x = 16
    so downstream speed = 16+4 = 20km/kr
  3. A person invests Rs 5800 in two schemes in such a way that he after 5 years and 4 years, he gets the same interest on respective parts. If the schemes offer 12% and 14% rate of interest respectively, what is the amount invested at 12% rate of interest?
    A) Rs 2200
    B) Rs 2800
    C) Rs 3600
    D) Rs 3000
    E) Rs 3200
    View Answer
     Option B
    Solution:

    Shortcut when interests are equal after t1 and t2 years:
    1/(t1*r1) : 1/(t2*r2)
    1/(5*12) : 1/(4*14)
    14 : 15
    So amount invested at 12% rate of interest = (14/29) * 5800 = 2800
  4. A trader bought an article at a discount of 10%. Then he sold the same article at 20% above the marked price of that article. What is the actual profit percent made by trader in this transaction?
    A) 16 2/3%
    B) 22%
    C) 31%
    D) 24 1/2%
    E) 33 1/3%
    View Answer
     Option E
    Solution:

    Let MP = 100, so CP for trader = Rs 90 (at 10% discount)
    And he sold at 20% above MP, so SP for trader = 120
    So profit% = (120-90)/90 * 100 = 100/3%
  5. The length and breadth of a rectangular park is 125m and 20m respectively. In the middle of the park is a circular lawn. If the area of rectangular park leaving the circular lawn is 1114 m<sup>2</sup>, what is the circumference of the circular lawn?
    A) 132 m
    B) 120 m
    C) 176 m
    D) 140 m
    E) 152 m
    View Answer
    Option A
    Solution:
    Area of park = 125*20 = 2500
    So area of circular lawn = 2500-1114 = 1386
    So ᴨr<sup>2</sup> = 1386
    Solve, r = 21
    So circumference = 2ᴨr = 2 * 22/7 * 21  
  6. There are two mixtures such that they contain 60% milk and 80% milk respectively. Some amount from first mixture is mixed with thrice the same amount of second mixture. Find the percentage of milk in the resultant mixture?
    A) 90%
    B) 75%
    C) 84%
    D) 80%
    E) 78%
    View Answer
     Option B
    Solution:

    Let x from first mixture, then 3x form second
    So milk from first = (60/100)*x, milk from second = (80/100)*3x
    So milk in resultant mixture is (60x/100) + (240x/100) = 3x
    Total mixture in third is x+3x = 4x
    So % of milk is (3x/4x)*100
  7. An amount invested compounded annually becomes Rs 4680 in 2 years and Rs 5616 in 3 years. What was the amount of money invested?
    A) Rs 3450
    B) Rs 3000
    C) Rs 3250
    D) Rs 4100
    E) Rs 3500
    View Answer
     Option C
    Solution:

    SI on 3380 for 1 yr = 5616 – 4680 = 936
    So rate = (100*936/4680*1) = 20
    So P (1 + 20/100)<sup>2</sup> = 4680
    Solve, P = 3250
  8. The train can cover a total distance of 1200 km from station A to station B and back to station A in a total of 19 hours. After reaching station B, the train halted for 1 hour. If the average speed of train from stations A to B is 25% more than that from station B to A, what is the speed of train from station A to station B?
    A) 50 km/hr
    B) 80 km/hr
    C) 60 km/hr
    D) 75 km/hr
    E) None of these
    View Answer
     Option D
    Solution:

    Let speed in return journey is x, then in A to B is (125/100)*x = 5x/4
    So 600/x + 600/(5x/4) = 18 [since total distance is 1200, so from one station to another is 600 each] Solve, x = 60
    So from A to B is 5*60/4
  9. A train started from point P at a speed of 50 km/hr. After 1 hour another train of same length started from point P at a speed of 60 km/hr in the same direction as the first one. After how much time the second train will meet the first train?
    A) 6 hours
    B) 5 hours
    C) 5.5 hours
    D) 360
    E) 320
    View Answer
    Option B
    Solution:

    Let first train meets after t hours when he started, so second train took (t-1) hours to reach the same distance.
    So distance covered by first train in t hours = distance covered by second train in (t-1) hours
    50*t = 60*(t-1)
    Solve, t = 6 hours
    So second train met first after (6-1) = 5 hours
  10. Two balls are drawn from an urn containing 6 red and 5 white balls one by one with replacement. What is the probability that both balls are different in color?
    A) 59/157
    B) 23/135
    C) 30/121
    D) 60/121
    E) None of these
    View Answer
     Option D
    Solution:
    Balls are drawn one by one so 2 cases:
    When first ball is red prob. = 6/11 * 5/11 = 30/121  [since replacement so 11 in both denominators] When first ball is white prob. = 5/11 * 6/11 = 30/121
    Add both cases
    So required probability = 30/121 + 30/121 = 60/121     

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