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  • RE: Discussion Room : Quant

    @vinaycat2017

    120 rupees is the original price
    25 rupees down payment means 95 rupees is what we are "Borrowing" from the shop.
    Amount paid in instalments = 25 * 4 = 100
    So 100 - 95 = 5 is the interest
    Now this interest gained (Rs 5) is through the interest gained in the available amount month by month.
    5 = 95R/(12 * 100) + 70R/(12 * 100) + 45R/(12 * 100) + 20R/(12 * 100)
    5 = 230R/(12 * 100)
    R = 6000/230 = 26.09%

    posted in Discussion Room
  • RE: CAT Question Bank - Time & Work

    @Ishita 120 is correct. Can you share your detailed approach so that others will benefit :)

    posted in Quant - Boosters
  • RE: CAT Question Bank - Time & Work

    @Ishita 22.5 is the right answer.

    A does 3x and B does x amount of work in a given amount of time.
    as work is inversely proportional to the time taken, A takes t days and B takes 3t days to complete a given amount of work.
    we know 3t - t = 60 days
    t = 30 days
    So A takes 30 days and B takes 30 + 60 = 90 days

    Together, 1/30 + 1/90 = 4/90 of work will be completed and it will take 90/4 = 22.5 days to finish the work together.

    posted in Quant - Boosters
  • RE: Gyan Room : Arithmetic - Concepts & Shortcuts

    If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:
    Sa/Sb = √(b/a)

    i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.

    Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 80kmph, find the rate at which the train B runs.

    Sa/Sb = √(4/9) = 2/3
    This gives us that the ratio of the speed of A : speed of B as 2 : 3.
    Since speed of A is 80 kmph, speed of B must be 80 * (3/2) = 120 kmph

    A and B start from Opladen and Cologne respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between Opladen and Cologne, A and B proceed to their destinations of Cologne and Opladen respectively. A reaches Cologne 40 minutes after the two meet and B reaches Opladen 90 minutes after their meeting. How long did A take to cover the distance between Opladen and Cologne?

    Sa/Sb = sqrt(90/40) = 3/2

    This gives us that the ratio of the speed of A : speed of B as 3:2. We know that time taken is inversely proportional to speed. If ratio of speed of A and B is 3:2, the time taken to travel the same distance will be in the ratio 2:3. Therefore, since B takes 90 mins to travel from the meeting point to Opladen, A must have taken 60 (= 90*2/3) mins to travel from Opladen to the meeting point

    So time taken by A to travel from Opladen to Cologne must be 60 + 40 mins = 1 hr 40 mins

    [Credits: Veritasprep]

    posted in Quant Primer
  • RE: Discussion Room : Quant

    @vinaycat2017
    Let the total distance be d
    truck started it journey with 100 kmph and continued so for distance d/3
    At d/3 it unloaded 150 cartons, so speed is increased by 20 + 20 + 400/100 = 44% (using successive percentage change formula)
    So d/3 distance covered at 100 kmph
    next d/3 distance covered at 144 kmph
    and last d/3 distance covered at 172 kmph
    average speed = 3abc/(ab + bc + ca) = 132 (approx)
    d = 132 * 9.82 = 1296 km (approx)

    posted in Discussion Room
  • RE: Discussion Room : Quant

    @deepalis727
    there are 299 numbers between 100 and 400 (excluding 100 and 400)
    Out of 299 numbers [299/2] = 149 numbers are divisible by 2
    Out of remaining 150 numbers [150/3] = 50 numbers are divisible by 3
    Out of remaining 100 numbers [100/5] = 20 numbers are divisible by 5
    Out of remaining 80 numbers [80/7] = 11 numbers are divisible by 7
    so 149 + 50 + 20 + 11 = 230 numbers are divisible by 2, 3, 5 or 7
    If it is including 100 and 400, then we have 232 numbers which are divisible by 2, 3, 5 or 7

    posted in Discussion Room
  • RE: CAT Question Bank - Time & Work

    @deepalis727 Cannot be determined due to insufficient data

    posted in Quant - Boosters
  • RE: CAT Question Bank - Time, Speed & Distance

    @manaswini Rohan's speed is 9 times than sohan.. so when Sohan completes 3 rounds, Rohan completes 3 * 9 = 27 rounds. 27 times ?

    posted in Quant - Boosters
  • RE: Question Bank - 100 CAT level questions on Time, Speed and Distance topic

    Funda : When running in the same direction : If the ratio of speeds of two athletes (in the most reducible form) is a : b, the number of distinct meeting points on the track would be would be |a – b|

    A and B will meet at |1 - 2| = 1 point.
    A and C will meet at |1 - 3| = 2 points
    A and D will meet at |1 - 4| = 3 points
    A and E will meet at |1 - 5| = 4 points
    A and F will meet at |1 - 6| = 5 points
    A and G will meet at |1 - 7| = 6 points
    So A will put 1 + 2 + 3 + 4 + 5 + 6 = 21 flags.

    similarly B and C will meet at |2 - 3| = 1 point
    B and D will meet at |2 - 4| = 2 points
    B and E will meet at |2 - 5| = 3 points
    B and F will meet at |2 - 6| = 4 points
    B and G will meet at |2 - 7| = 5 points
    So B will put 1 + 2 + 3 + 4 + 5 = 15 flags

    Similarly find for C, D, E and F.

    We will get 21 + 15 + 10 + 6 + 3 + 1 = 56 flags

    posted in Quant BBQ - Best of Best Questions
  • RE: Question Bank - 100 CAT level questions on Time, Speed and Distance topic

    Let the distance PQ be d and speed of river be R and speed of boat be B
    d/(B + R) = 4
    d/(B - R) = 6
    Solve for B.
    4(B + R) = 6(B - R)
    4B + 4R = 6B - 6R
    10R = 2B
    R = B/5
    d/(B + B/5) = d/(6B/5) = 5d/6B = 4
    d = 24B/5

    If we put d = 24 units, then B = 5 and R = 1
    So first hour boat will cover 6 units, second hour boat will cover 5 * 1.4 + 1 = 8 units and third hour 10 units.

    So 24 units will be covered in 3 hours

    posted in Quant BBQ - Best of Best Questions

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