Mixed Quantitative Aptitude Questions Set 52

  1. A boat goes 24 km upstream and 54 km downstream in 6 hrs. In 8 hrs, it can go 36 km upstream and 48 km downstream. The speed (in km/hr) of the boat in still water is:
    A) 21
    B) 19.5
    C) 13.75
    D) 18
    E) None
    View Answer
    Option B
    Solution:
    General method
    24/u-v+54/u+v=6—1
    36/u-v+48/u+v=8—2
    By solving 1 and 2 we got the ans.
    Shortcut
    U/s…………..D/s……….t
    24……………..54………..6      common terms cut= 4 9 1
    36……………..48………..8                                           9 12 2
    u/s= (4*12)-(9*9)/(9*2)-(12*1) ==u/s=33/6=5.5
    d/s=(4*12)-(9*9)/(4*2)-(9*1) ==d/s=33/1=33
    then U=(33+5.5)/2=38.5/2=19.25
    V= (33-5.5)/2=27.5/2=13.75
  2. A boat takes 30 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 5 km/hr and the speed of the boat in still water is 10 km/hr, what is the distance between A and B?
    A) 146km
    B) 150km
    C) 180km
    D) 190km
    E) None
    View Answer
    Option C
    Solution:

    Downstream speed= 10+5 = 15
    Upstream speed = 10-5 = 5
    Now total time is 30 hours
    If distance between A and B is d, then distance BC = d/2
    Now distance/speed = time, so
    d/15 + (d/2)/5= 30
    Solve, d = 180 km.
  3. A boat takes 150 min less to travel 40 km downstream than to travel the same distance upstream. The speed of the stream is 4 km/hr. What is the downstream speed?
    A) 16 km/hr
    B) 12 km/hr
    C) 10 km/hr
    D) 8 km/hr
    E) None
    View Answer
    Option A
    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 40 km downstream = time to travel 40 km upstream – 150/60
    So 40/(x+4) = 40/(x-4) – 5/2
    8/(x-4) – 8/(x+4) = 1/2
    x+4 – (x-4)/(x2 – 16) = 1/16
    solve, x = 12
    so downstream speed = 12+4=16km/hr.
  4. Two pipes can fill a tank with water in 15 and 12 hours respectively and a third pipe can empty it in 4 hours. If the pipes be opened in order at 10, 11 and 1 p.m. respectively, the tank will be emptied at
    A) 11 : 40 a.m.
    B) 12 : 40 p.m.
    C) 4.40p.m.
    D) 2.40p.m.
    E) None
    View Answer
    Option C
    Solution:

    Let tank will be emptied in x hrs after 10am
    x/15 + (x-1)/12 – (x-3)/4 =0
    x = 40/6 = 6 2/3hrs = 6hrs 40min
    Then It will be emptied in 10+6.40=4.40p.m.
  5. Pipes A and B can fill a tank in 10 and 12 hours respectively. Pipe C can empty it in 20 hours. If all the three pipes are opened together, then the tank will be filled in (in hours):
    A) 7
    B) 5.25
    C) 6
    D) 7.30
    E) None
    View Answer
    Option D
    Solution:

    Pipes A,B,C filled together in 1 hour
    =1/10 + 1/12 − 1/20 = (11-3)/60 8 /60
    Tank filled in 60/8 = 7 ½.
  6. An army lost 10% its men in war, 10% of the remaining due to diseases died and 10% of the rest were disabled. Thus, the strength was reduced to 729000 active men. Find the original strength.
    A) 10 Lakh
    B) 12Lakh
    C) 15Lakh
    D) 18Lakh
    E) None
    View Answer
    Option A
    Solution:

    Let army has 100 men.
    10% loss in war, so remained are 90 men
    then,10% of 90 died due to diseases, remained 90-9 = 81
    then again, 10% of 81 again disabled
    So, remained men = 90% of 81
    90% of 81 = 729000
    (90×81)/100 =729000
    1= 10000
    100 = 1000000
    then total men are 10,00,000.
  7. Weights of two friends P and Q are in the ratio 4:5. If P’s weight is increased by 10% and total weight of P and Q become 82.8 kg, with an increases of 15%. By what percent did the weight of Q has to be increased?
    A) 19%
    B) 22%
    C) 17.5%
    D) 12.5%
    E) None
    View Answer
    Option A
    Solution:

    10……………..x
    ……….15
    x-15 : 15-10
    Now, given ratio of P and Q’s weight = 4:5
    Hence, (x-15)/(15-10) = 4/5
    x = 19%.
  8. A shopkeeper sold a T.V. set for Rs. 17,940 with a discount of 8% and earned a profit of 19.6% . What would have been the percentage of earned if no discount was offered ?
    A) 25%
    B) 30%
    C) 22.5%
    D) 40%
    E) None
    View Answer
    Option B
    Solution:

    SP=Rs 17,940.
    MP =17940*100/92=19500
    CP=17940*100/119.6=15000
    So profit without discount= 19500-15000=4500
  9. Fresh grapes contain 80% water, while dry grapes contain 10% water. If the weight of dry grapes is 500 kg, then what is its total weight (in kg) when it is fresh?
    A) 2000
    B) 2200
    C) 2250
    D) 2800
    E) None
    View Answer
    Option C
    Solution:

    weight of dry grapes = 500 kg
    Since dry grapes contain 10% of water, weight of grape pulp in 500 kg of dry grapes
    = 90% of 500 = 450 kg
    Let x be its total weight when it is fresh.
    Fresh grapes contain 80% water. Therefore, 20% of x is 450 kg
    100% of x = 450 × 5 = 2250
  10. If a 36 inches long strip cloth shrinks to 33 inches after being washed, how many inches long will the same strip remain after washing if it were 48 inches long?
    A) 44 inches
    B) 46 inches
    C) 55 inches
    D) 60 inches
    E) None
    View Answer
    Option A
    Solution:

    Shrinking of cloth,
    = [(36-33)/36]*100.
    = 100/12%
    Second time the strip shrinks,
    = (48*100)/1200 = 4 inches
    hence , the cloth remains = 48-4 = 44.

 

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3 Thoughts to “Mixed Quantitative Aptitude Questions Set 52”

  1. LIC AAO 2018

    Dear az please provide weekly CA quiz October 2nd week

    1. karthik

      A boat takes 150 min less to travel 40 km downstream than to travel the same distance upstream. The speed of the stream is 4 km/hr. What is the downstream speed?

      here: Time to travel 40 km downstream = time to travel 40 km upstream – 150/60

      Time to travel 40 km downstream = time to travel 40 km upstream + 150/60

  2. karthik

    first one 12.5

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