Question Bank - Arithmetic - Shashank Prabhu, CAT 100 Percentiler



  • Q14) The average marks scored by two groups X and Y of students are 70 and 75 respectively. Four students are moved from group Y to group X, thereby interchanging the average marks of the two groups. Find the total number of students in two groups put together, if the average marks scored by the four students who moved are 85.

    [OA: 20]



  • Q17) In a race there were ten athletes running the race and no two of them finished the race in the same position. If there were three girls in the race, what is the probability that the worst position among the girls is five?

    [OA: 1/20]



  • Q30) If Rs. 1000 is invested at an interest rate of 5% p.a. and the interest earned is added to the principal every 10 years, then after how many years will the amount become Rs.2000?
    a) 20/3
    b) 50/3
    c) 25/4
    d) None of these

    [OA: Option b]



  • Q31) A train after travelling for a certain distance develops a problem and decreases its speed to half its original speed and reaches its destination 45 minutes late. Had the problem occurred 30 km further on, it would have reached its destination 15 minutes earlier. What is the speed of the train (in m/s)?

    [OA: 100/3 m/s]



  • Q32) Each person in a group of 110 investors has investments in either equities or securities or both. Exactly 25% of the investors in equities have investments in securities, and exactly 40% of the investors in securities have investments in equities. How many have investments in equities?

    [OA: 80]



  • Q36) A can complete 2/3rd of a piece of work in 48 days. A and B when working together right from the beginning can complete 3/4th of the work in 18 days. How many days will B require to finish the work alone?

    [OA: 36]



  • Q56) 12 men can finish a job in 16 days. 5 men were working at the start and after 8 days, 3 men were added. How many days will it take to finish the whole job?

    [OA: 27]



  • Q59) A retail bookseller buys books at 58% of the list price. He expects to earn a minimum of 20% net profit on his selling price. What is the maximum discount that he can offer to his customer?
    (a) 31.6%
    (b) 25.5%
    (c) 27.5%
    (d) 30%
    (e) 28.5%

    [OA: 27.5%]



  • Q61) On buying a camera, the shopkeeper gives three rolls of film free. On buying a camera and six rolls of film, the shopkeeper gives additional four rolls of film free. If the equivalent discount is the same in both cases, then how many rolls will be equal in value to a camera?

    [OA: 18]



  • Q62) A mixture of liquids A and B contains 70% of B by weight. Liquid C is added till the final solution contains 12% by weight of A. What is the ratio (by weight) of B to C in the final mixture?

    [OA: 7:15]



  • Q78) Sukriti and Saloni are athletes. Sukriti covers a distance of 1 km in 5 minutes and 50 seconds, while Saloni covers the same distance in 6 minutes and 4 seconds. If both of them start together and run at uniform speed, by what distance (approximately) will Sukriti win a 5 km mini marathon:
    a. 150 m
    b. 200 m
    c. 175 m
    d. 225 m.

    [OA: Option b]



  • Q80) Aditya, Vedus and Yuvraj alone can do a job in 6 weeks, 9 weeks and 12 weeks respectively. They work together for 2 weeks. Then Aditya leaves the job. Vedus leaves the job a week earlier to the completion of the work. The job would be completed in:
    a. 4 weeks
    b. 5 weeks
    c. 7 weeks
    d. None of the above.

    [OA: Option a]



  • Q85) A and B, who are separated by a distance 90 m, are approaching towards each other. The initial speed of A is 5 m/s and that of B is 10 m/s. If A increases his speed by 5 m/s every second, when will they meet each other?

    [OA: 4 seconds]



  • Q86) In 2017, the price of commodities A and B witnessed an increase of 24% and 18% respectively over the previous year. If the prices of the two commodities were the same in 2017, what was the ratio of the price of B to A in 2016?
    (a) 62:59
    (b) 59:62
    (c) 41:38
    (d) 38:41

    [OA: Option a]



  • Q89) The average marks obtained by the candidates who passed and those who failed in an examination are 60 and 25 respectively. The average marks obtained by all the candidates who appeared for the examination is more than 43 but not more than 49.

    1. The number of candidates who passed as a fraction of the total number of candidates who appeared for the examination could never be
      (a) 3/5
      (b) 4/7
      (c) 18/35
      (d) 24/35

    2. The minimum possible total marks obtained by all the candidates in the examination could be
      (a) 150
      (b) 85
      (c) 110
      (d) 145

    [OA: 1 - C, 2 - D]



  • Q94) A yearly payment to the servant is Rs. 90 plus one turban. The servant leaves the job after 9 months and receives Rs. 65 and a turban. Then find the price of the turban.

    [OA: 10]



  • Q95) Distance between A and B is 72 km. Two men started walking from A and B at the same time towards each other. The person who started from A travelled uniformly with average speed of 4 km/hr. While the other man travelled with varying speed as follows: in the first hour his speed was 2 km/hr, in the second hour it was 2.5 km/hr, in the third hour it was 3 km/hr, and so on. Which of the following will be true about the meeting point when they meet each other?
    a. Meet after 7 hrs
    b. Meet after 10 hrs
    c. Meet at 35 km from A
    d. Meet mid-way between A and B

    [OA: Option d]



  • Q97) One bacterium splits into eight bacteria of the next generation. But due to environmental condition only 50% survive and remaining 50% dies after producing next generation. If the seventh generation number is 4,096 million, what is the number in first generation?

    [OA: 1 million]



  • Q2) A, B, C and D are four friends each of whom weighs less than 100 kg. From among them they form a group and find the total weight of that group. If the sum of the total weights of all possible distinct groups, each having the same number of members as in the first is 882 kg, then the average weight of the four friends is
    (1) 41.75 kg
    (2) 63.5 kg
    (3) 73.5 kg
    (4) Cannot be determined

    [OA: Option 3]



  • Q4) Each of Amit, Bosco, Chris and Deepak bought 56 pencils out of which a total of 64 pencils were found to be broken. If the number of unbroken pencils with Chris is 60% and 75% more than Amit and Bosco respectively, then find the number of broken pencils with Deepak.

    [OA: 19]


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