Solved CAT Questions (Arithmetic) - Set 7


  • Skadoooosh!!!


    Q1. (CAT 1996)
    Instead of a metre scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20% on cash payment, what is his overall profit percentage?
    a. 20%
    b. 25%
    c. 40%
    d. 15%

    Let price of 1 meter is 100
    Merchant bought 1200 cm for 100 and he sells 800 cm for 80
    Selling price of 1200 cm is 1200 x 80/800 = 120
    Profit percentage is 20%

    Q2. (CAT 1996)
    The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1 : 2 : 3 : 4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond.
    a. Rs. 1.4 lakh
    b. Rs. 2 lakh
    c. Rs. 1 lakh
    d. Rs. 2.1 lakh

    If we assume weight of diamond 10x. Well I came up with 10x because the ratio given 1 : 2 : 3 : 4 adds upto 10.
    So individual weights of diamonds will be x, 2x, 3x and 4x
    original price = k(10x)^2
    Price for pieces = k(x^2 + 4x^2 + 9x^2 + 16x^2) = k30x^2
    Thus change in price we see is 100kx^2 - 30kx^2 = 70kx^2 which is given as 70,000
    Thus the original price 100kx^2 will be 1,00,000
    will be 1,00,000

    Q3. (CAT 1996)
    In a mile race, Akshay can be given a start of 128 m by Bhairav. If Bhairav can give Chinmay a start of 4 m in a 100 m dash, then who out of Akshay and chinmay will win a race of one and half miles and what will be the final lead given by the winner to the loser? (One mile is 1600 m)
    (a) Akshay, 1/2 mile
    (b) Chinmay, 1/32 mile
    (c) Akshay, 1/24 mile
    (d) Chinmay, 1/16 mile

    B will cover 1600m when A covers 1600 – 128 = 1472m
    Let the time taken be t
    Speed of B= 1600/t
    Speed of A= 1472/t
    Speed of B/ Speed of A= 1600 / 1472 = 25/23 --------- (1)
    Similarly
    Speed of B / Speed of C = 100/96 = 25/24 --------- (2)
    From (1) and (2)
    Speed of A / Speed of C = 23/24
    Let speed of A = 23x, then Speed of C = 24x
    Time taken by C to complete one and half miles race = (1600 x 1.5)/24x = 100/x
    In same time distance covered by A = 100/x * 23x = 2300m
    Therefore lead = 2400 – 2300
    = 100 m
    = 1/16 mile
    Therefore winner is C by 1/16 mile

    Q4. (CAT 1996)
    Two liquids A and B are in the ratio 5 : 1 in container 1 and 1 : 3 in container 2. In what ratio should the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio 1 : 1?
    a. 2 : 3
    b. 4 : 3
    c. 3 : 2
    d. 3 : 4

    Take 1 portion from container 1 and N portions from container 2.
    Then we collect total 5A/6 + B/6 + N(3B/4 + A/4)
    Ratio of A and B in the new mix is (5/6 + N/4)A : (3N/4 + 1/6)B
    for A : B = 1 : 1, the coefficients of A and B must be equal
    (5/6 + N/4) = (3N/4 + 1/6)
    N = 4/3
    So the required ratio is 1 : 4/3 = 3 : 4

    Q5. (CAT 1996)
    A man travels three-fifths of a distance AB at a speed 3a, and the remaining at a speed 2b. If he goes from B to A and return at a speed 5c in the same time, then
    a) 1/a + 1/b = 1/c
    b) a + b = c
    c) 1/a + 1/b = 2/c
    d) None of these

    Let distance between A and B = d
    Time taken to cover 3d/5 = (3d/5)/3a = d/5a
    Time taken to cover remaining distance = (2d/5)/2b = d/5b
    Time taken to go from B to A and then return to B = 2d/5c
    Now, d/5a + d/5b = 2d/5c
    1/a + 1/b = 2/c

    Q6. (CAT 1996)
    A man travels from A to B at a speed x km/hr. He then rests at B for x hours. He then travels from B to C at a speed 2x km/hr and rests for 2x hours. He moves further to D at a speed twice as that between B and C. He thus reaches D in 16 hr. If distances A-B, B-C and C-D are all equal to 12 km, the time for which he rested at B could be
    a. 3 hr
    b. 6 hr
    c. 2 hr
    d. 4 hr

    Total time taken = Time taken for each stretch + rest time between stretches = 16
    (12/x) + x + (12/2x) + 2x + (12/4x) = 16
    12/x + x + 1/6x + 2x + 1/3x = 16
    3x^2 - 16x + 21 = 0
    x = 3 hours

    Q7. (CAT 1996)
    The price of a Maruti car rises by 30% while the sales of the car come down by 20%. What is the percentage change in the total revenue?
    a. –4%
    b. –2%
    c. +4%
    d. +2%

    Let say 100 cars were sold before for a price of 100 rupee each.
    So total revenue before = 10000
    Now car price is 130 and sale is 80. Total revenue = 10400
    Percentage change = + 4%

    Q8. (CAT 1996)
    In a watch, the minute hand crosses the hour hand for the third time exactly after every 3 hr 18 min and 15 s of watch time. What is the time gained or lost by this watch in one day?
    a. 14 min 10 s lost
    b. 13 min 50 s lost
    c. 13 min 20 s gained
    d. 14 min 40 s gained

    Remember this point - In a normal watch, minute hand crosses hour hand every 1 hour 5 minutes and 27 seconds ( which is equal to 720/11 minutes or ~ 3930 seconds)
    So to cross thrice, a correct watch would take - 3 hours 16 minutes and 21 seconds
    Here it took 3 hours 18 minutes and 15 seconds, means it is losing time. (1 minute and 54 seconds for every 3 hours 18 minutes and 15 seconds)
    So the time lost in a day (24 hours) is approximately 13 minutes 50 seconds.

    Q9. (CAT 1996)
    I sold two watches for Rs. 300 each, one at the loss of 10% and the other at the profit of 10%. What is the percentage of loss (–) or profit (+) that resulted from the transaction?
    a. (+) 10
    b. (–) 1
    c. (+) 1
    d. (–) 10

    Formula - If we sell an item at the same price, one at a profit of x% and another at a loss of x%, then the net result is LOSS of (x/10)^2
    here x = 10 so it is a loss of (10/10)^2 = Loss of 1 = ( - 1 )

    Q10. (CAT 1995)
    A man invests Rs. 3,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?
    a. Rs. 1,200
    b. Rs. 1,300
    c. Rs. 1,500
    d. Rs. 2,000

    Use Alligation
    Present rate of interest = 5% (Cheaper quantity)
    New rate of interest = 8% (Dearer Quantity)
    Mean rate of interest = 6%
    Ratio of Dearer Value : Cheaper Value = m - c : d - m = 6 - 5 : 8 - 6 = 1 : 2
    Dearer Value = Rs.3000/2 = Rs.1500


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