MathOratory - Quant notes - Set 5

  • IIM Lucknow | MathOratory

    The difference between the compound interest (compounded annually) and simple interest at the same rate of interest p.a. on Rs. 10000 principal for 2 years is Rs. 144. The rate of interest is:

    For simple interest, we will have r + r = 2r% interest generated.
    For compound interest, we will have (r + r + r²/100)%
    So the difference will be r²/100 %
    Thus r²/100% of 10000 = 144
    Or, r = 12

    16 men and 6 women finished a piece of work in 16 days. 4 men and 24 women can also finish the same piece of work in 16 days. How many days will 12 men and 12 women take to finish the same piece of work?

    If we consider the efficiencies of each man and woman to be m and w respectively
    Then the first group of workers will have a net efficiency of 16m + 6w
    And the second group will have a net efficiency of 4m + 24w
    As the first group finishes the work in 16 days, total work = (16m + 6w) * 16
    And same with respect to the second group = (4m + 24w) * 16
    Equating the total work
    (16m+6w) * 16 = (4m+24w) * 16
    m/w = 3/2
    So we can assume the efficiency of each man to be 3 and that of each woman to be 2
    So total work = (16 * 3 + 6 * 2) * 16 = 60 * 16
    Now when 12 men and 12 women are working, net efficiency per day = 12 * 3 + 12 * 2 = 60
    Time required = 60*16/60 = 16 days
    Note: I have provided the generic process of these types

    220 chocolates were distributed among 80 boys and girls such that each boy gets 4 chocolates and each girl gets 2 chocolates. Find the difference between the number of boys and the girls.

    If all were boys, then total chocolates would have been 320
    But it is 100 less
    Every boy replaced with girl, drop of 2 chocolates.. So 50 times we need the drop
    So 50 girls and rest 30 boys
    Difference is 20

    The micromanometer in a certain factory can measure the pressure inside the gas chamber from 1 unit to 999999 units. Lately this instrument has not been working properly. The problem with the instrument is that it always skips the digit 5 and moves directly from 4 to 6. What is the actual pressure inside the gas chamber if the micromanometer displays 003016?

    One digit missing implies 9 digits .. implies base 9
    The only difference is the correspondence of this number system and the base 9 system, where the digits are different
    So in this number system, the digits are
    But in base 9, the digits are
    So using the above correspondence: 3016 in this number system will be 3015 in base 9
    3015 in base 9 implies 3 * 9^3 + 1 * 9 + 6 = 2201

    N = 7777....7777(7 repeats itself 429 times). Find the remainder when N is divided by 1144

    1144 = 11 * 8 * 13
    Any digit repeated even number of times is a multiple of 11
    Any 6 digits number of the form abcabc = abc*1001, will be a multiple of 1001 and hence a multiple of 13 ...
    If the last 3 digits of the number is divisible by 8, then the number is divisible by 8, as 1000 is a multiple of 8
    If we separate the last 3 digits of the above number, we are left with 426 sevens followed by 3 zeroes ...
    426 is an even number hence the number is a multiple of 11
    426 is a multiple of 6, hence we can group the number into multple groups of 777777, which is of the form abcabc, hence multiple of 13
    As, the last 3 digits are 000, the number should also be a,multiple of 8
    So, the remainder will be given by the 777 that we have taken out, as the remaining part is divisible by 11, 13 and 8 => divisible by 1144
    777 divided by 1144, remainder is 777 (answer)

    Mr. Ghosh arrives at his office 30 min late everyday. On a particular day he reduces his speed by 25% and hence reached 50 mins late instead.
    (a) Find how much time would he take to travel to his office if he decides to be on time.
    (b) If he has to arrive on time, by what % should he increase his speed
    (Assuming he starts from his home everyday at the same time)

    As he is reducing his speed by 25%, the speed becomes 75% or 3/4
    So time should become 4/3, or increases by 1/3... So that 1/3 increase corresponds to an increase of 20 mins (30 to 50 mins late)
    Thus time taken to travel in the previous speed is 20*3 = 60 mins...
    Now as he reaches 30 mins late, he needs to drop his total time by 30 mins to reach on time, or he needs to reach in 60 - 30 = 30 mins (answer to the first part)
    Now, instead of reaching in 60 mins, he has to reach in 30 mins. Or, he has to half his time and in order to halve the time, one would need to double the speed... Or in other words, increase the speed by 100%

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