Practice questions for CAT - Arithmetics


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    Credits : Anuj Kumar Sinha

    By selling 1000 books at 50 for a rupee a man lost 40%.How many shall he sell for a rupee to gain 20% ?

    Soln: 40% loss means sp=60% of cp
    Now he wants 20% profit means sp = 120% of cp
    so sp should be doubled, means instead of selling 50 books for a rupee, he should sell them 50 books for 2 rupees means 25 books/rupee.

    A book was sold for a certain sum and thre was a loss of 20%. Had it been sold for Rs. 12 more, there would have been a gain of 30%. What would be the profit if the book were sold for Rs 4.8 more than what it was actually sold for ?

    Soln:from 20% loss to 30 % profit, difference is +30 –(-20) = 50%
    50% difference = 12 rupees
    so 100%=cp=24 rupees
    now 20% loss on cp = 20% of 24=4.8 rupees loss

    If book was sold at 4.8 more this loss would be compensated and finally no loss no profit.

    A BMW and a nano are travelling along a straight road. BMW overtakes nano at 9am and continues travelling till 1pm and then it returns backward and meet nano at 2pm. At what time nano will reach the point where BMW turned back.

    Soln: BMW travelled 4 hrs ahead and 1 hr backward so net is 3hr ahead it travelled and in mean time nano travelled 5hrs ahead and yet they r at same point. It means ratio of speed of BMW:nano=5:3
    When distance is constant time is inversely proportional to speed hence time ratio:3:5
    So, BMW took 4 hrs to reach turning point. Hence, nano will take 4*(5/3)=20/3 hrs to reach that point. So it will reach at 9am + 20/3 hrs =3:40 pm

    Ironman can do a job in 20 days and Thor can do in 25 days. They started working together and few days later Hawkey joined them and thus all completed the work in 10 days. If total remuneration was 5000, find Thor’s share

    Soln: Ironman  does 5% work in one day. Thor does  4% ork in one day. 10 days mein 90% by both together. Hawkey does remaining 10%. Ratio of work done 5:4:1. So Thor’s  share=4*5000/(1+4+5)=2000

    A says to B ”I am 4 times as old as you were when I was as old as you are now.” B replies ”10 yrs back I was 9 yrs younger to you". How old is B?

    Soln: from line 2= > A = 9+B
    from line 1= > A=4(A-18 )= > 3A=72= > A=24 so B=15
    A says I am 4 of your age  when i am as old as you are now. What is B’s age right now?? 9 years less than A
    when  A is of that age as B is now... then B will be 18 years younger than A’s current age....
    means B ‘s age that time will be (A-18 )
    then according to que A = 4(A-18 )

    4 parties Congress,BJP,AAP and BSP contested for all seats in an election.Each seat was won by exactly one of the 4 parties. Congress lost on 29 seats, BJP lost on 12 seats, AAP lost on 20 seats and BSP lost on 26 seats.What was the total no of seats being contested in the election?

    Soln: for each seat there is 1 win and 3 losses
    so total no of losses = 87 means no of seats = 87/3=29

    Contractor undertakes to dig 10km long canal in 180 days and employs 40 men. After 60 days they finished only 2.5km of canal.To complete the wirk on time, how much more men needs to be hired?

    Soln: Work done = 2.5  left=7.5  (3 times)
    time = 60 days left=120 days(2 times)
    so to do 3 times work in 2 times time, need 3/2 times men
    3*40/2 = 60 men
    so 6-40=20 more men needs to be hired.

    There are 3 runners Aman, Badal and Carol. Aman beats Badal by 20m amd Carol by 34m. Badal beats Carol by 21m. Find length of race.

    Soln : While Badal travelled 20m, Carol travelled 34-21=13m
    so speed ratio B:C=20:13
    so B/C = 20/13 = (L-20)/(L-34)
    L=60m

    I wanted to buy 2 dozen bananas but I am 30 Rupees short. So I bought 20 bananas and 2 rupees is left with me. Price of 1 banana?

    Soln : 24 bananas cost= > 30 more than what I have
    20 bananas cost = > 2 less than what I have
    So 4 bananas cost 30+2=32rupees
    1 banana cost 8 rupees

    100 kg grapes contains 98% water. After few days, due to evaporation some water evaporates and it contains 94% of water. Find weight of grapes.

    Soln : 98% water means 2% mass=2kg mass
    When water evaporates, water=94% so mass =6%
    but mass is constant so 2 kg = 6%
    Numerator(mass)  is same but fraction increased 3 times. So denominator decreased 3 times
    100/3 = 33.33 kg new weight of grapes.

     


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