CAT Question Bank - Arithmetic



  • total =1000ml
    Water =850ml
    Juice = 150ml
    Now we are adding water that means juice is still untouched and it's given that now juice is 1 % of the quantity
    Clearly
    Total = 15000ml
    Juice = 150 ml
    So water = 14850ml
    Water added = 14850-850 = 14000ml I.e 14ltr
    [solved by rajendra rajput]



  • Q3) Person A can do a piece of work in 20 days. He works at it for 5 days and then person B finishes it in 10 more days. How many days will they need, in order to finish the work together?



  • A work for 5 days , so he work 5/20 = 1/4 work
    Remaining 3/4 is done by B in 10 days
    So B take 10*4/3 = 40/3 days

    Together
    1/20 + 3/40
    = 5/40
    = 1/8
    = 8 days
    [solved by rajendra rajput]



  • Q4) Ram and Shayam run a race of 2000m. First, Ram gives Shayam a start of 200m and beats him by 30 seconds. Next Ram gives Shayam a lead of 3 minutes and gets beaten by 1000m. What is the time in minutes in which Ram and Shayam can run the race separately?



  • Let the speed of Ram be "R" & Shyam be "S"

    Condition 1:-
    When shyam gets head start of 200m and beaten by 30 sec
    2000/R - 1800/S = 30 ---> eq (1)

    Condition 2:-
    When shyam gets a head start of 3 min and won by 1000m
    1000/R - 2000/S = 180 ---> eq (2)

    Solving this we will get
    R = 25/3 m/s
    S = 20/3 m/s

    R = 2000 * 3 * /25 = 4 min
    S = 2000 * 3/20 = 5 min

    Thus time taken by Ram & Shyam to complete the race is 4 min & 5 min

    [solved by rajendra rajput]



  • Q5) A cistern is filled in 6h but take 4h longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in how much time?



  • With a leak it takes 10 hr to fill the tank
    1/6 - 1/x = 1/10
    1/x = 1/6 - 1/10
    1/x = 4/60
    1/x = 1/15
    X = 15 hrs

    [solved by rajendra rajput]



  • Q6) A take 5 days more than B to do a job & 9 days more than C; A & B together can do the job in the same time as C. How many days A would take to do it?



  • Clearly
    1/A + 1/B = 1/C
    1/A + 1/(A-5) = 1/(A-9)
    Solve this quadratic
    You will get
    A = 15 Days

    [solved by rajendra rajput]



  • Q7) The vessels contain water and milk in the ratio 1:2 and 2:5 are mixed in the ration is 1:4 then what will be the resulting ratio?



  • Quantity of water in the resultant mixture
    1 * 1/3 + 4 * 2/7 = 1/3 + 8/7 = 31/21

    Quantity of milk in the resultant mixture
    1 * 2/3 + 4 * 5/7 = 2/3 + 20/7 = 74/21

    Required ratio
    31/21 : 74/21
    = 31 : 74

    [solved by rajendra rajput]



  • Q8) Ram and Shyam start at same end of a swimming competition.The length of pool is 50m.The race is for completing 1000m. If Ram beats Shyam and meets him 17 times during the race what could be the speed of Shyam if speed of Ram is 5m/s?



  • Length of pool is 50m
    So 100m (2x of pool)
    Since they meet 17 times
    So ram covers 17 * 100 = 1700 m
    But race is of 1000m
    When ram covers the race I.e 1000m
    So shyam covers 1700-1000 = 700m
    Ram ---- shyam
    1000----> 700
    5 ------> ?
    5 * 700/1000
    = 3.5 m/s

    [solved by rajendra rajput]



  • Q9) A and B can finish a work together in 12 days, and B and C together in 16 days. If A alone works for 5 days and then B alone continues for 7 days, then remaining work is done by C in 13 days. In how many days can C alone finish the complete work?



  • Lcm of (12,16) = 48 units < -- total work
    So A+B = 48/12 = 4 units per day
    B+C = 48/16 = 3 units per day
    Now,
    5A+7B+13C = 48 units
    5 (A+B)+2 (B+C)+11C = 48
    5 (4)+2 (3)+11C = 48
    20+6+11C = 48
    11C = 22
    C = 2 units
    So C does 2 units of work daily
    So total time required to complete work alone is 48/2 = 24 days

    [solved by rajendra rajput]



  • Q10) Around a circular path of 360km, three men start cycling at 48, 60 and 72 km per day. After how many days will they meet?



  • The time each takes to complete a round of circular field,
    360/48 = 7.5
    360/60 = 6
    360/72 = 5 days.
    They'll meet at the time equal to the LCM of (7.5,6,2)
    which is 30 days.

    [solved by rajendra rajput]



  • Q11) Read the information below and answer the questions that follow: Harsh and his son Rakesh go for running in a park. The track is circular with a circumference of 600m. They run with a constant speeds of 7m/s and 5m/s respectively. They start from the same point but run in opposite directions till they meet each other at the starting point. Then they start running in the same direction till they meet again at the starting point.

    For what duration do they run?
    a) 5 minutes
    b) 10 minutes
    c) 15 minutes
    d) 20 minutes

    What is the distance covered by Rakesh during the entire session?
    a) 4 km
    b) 5 km
    c) 6 km
    d) 8 km



    1. When they run in the opposite direction:
      Relative speed = 12 m/s.
      So they meet every 600/12 = 50 seconds.
      When they meet for the first time, harsh would have run 350m and Rakesh 250m.
      LCM of 350 and 600 = 4200
      LCM of 250 and 600 = 3000
      So they’ll meet at the starting point after covering a total distance of 7200m
      Time taken = 4200/7 = 600 sec.
      When they run in the same direction:
      Relative speed = 2 m/s.
      So they meet every 600/2 = 300 seconds.
      When they meet for the first time, harsh would have run 2100m and Rakesh 1500m.
      LCM of 2100 and 600 = 4200
      LCM of 1500 and 600 = 3000
      So they’ll meet at the starting point for the second time after covering a total distance of 7200m.
      Time taken = 4200/7 = 600 sec.
      Total duration = 1200 sec = 20 min.

    2. Since both of them ran for 20 minutes, distance covered by Rakesh
      = 5x20x60 = 6000m = 6km

    [solved by ADURO team]



  • Q12) Two shooters who are 510m apart shoot a bullet each whose speeds are in the ratio 8:15. The bullets collide at right angle after 3 seconds and are reflected by 90 degrees with respect to their original direction. The speed of the first bullet remains the same while the speed of the second bullet is reduced by 60%. How far are the bullets from each other five seconds after their collision?
    a) 400 m
    b) 500 m
    c) 600 m
    d) 700 m


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