Mixed Quantitative Aptitude Questions Set 3

 

  1. The average age of Abhilasha and Aadhira is 35 years. If Aaloka replaces Abhilasha, the average age is 31 years, if Aaloka replaces Aadhira average age is 36 years. If the average age of Aditi and Aashirya is half of average age of Abhilasha, Aadhira and Aaloka. then average age of all the five people is
    A) 28.2 years
    B) 32,4 years
    C) 27.2 years
    D) 30.2 years
    E) None of these
    View Answer
    Option C
    Solution:
    Abhilasha, Aadhira, Aaloka, Aditi, Aashirya – X, Y, Z, P, Q
    X + Y = 35 * 2 =70 –(1)
    Z + Y = 31 * 2 =62 –(2)
    X + Z = 36 * 2 = 72 –(3)
    From (1) (2) and (3)
    X = 40 ; y =30; Z = 32
    Average age of P and Q =1/2 * [( X + Y + Z)/3]
    = 102/6 = 17
    Sum of the age of P and Q = 34
    Average age of all the five people = (34 + 102)/5 = 27.2
  2. The average score of a cricket player after 24 innings is 25 and in the 25th innings the player scores 25 runs. In the 26th innings what minimum number of runs will be required to increase his average score by 2 than it was before the 26th innings?
    A) 64
    B) 57
    C) 44
    D) 77
    E) None of these
    View Answer
    Option D
    Solution:
    The average score of a cricket player after 25th Innings = (24 * 25 + 25) / 25 = 25
    Required Run = X
    (625 + X)/26 =27
    X = 26 * 27 – 625 = 77
  3. There are two vessels P and Q filled with cooking oil with different prices and with volumes 160 and 40 liters respectively. Equal quantities are drawn from both P and Q in such a manner that the cooking oil drawn from P is poured in into Q and oil drawn from Q is poured into P. If the price per liter becomes equal in both vessels. What is the (equal) quantity that was drawn from both P and Q?
    A) 52 litre
    B) 32 litre
    C) 42 litre
    D) 62 litre
    E) None of these
    View Answer
    Option B
    Solution:
    Vessel (P)                          Vessel (Q)
    Quantity= 160 l                  Quantity= 40 l
    rate – p                                rate – q
    Let quantity taken out from both = a litres
    ‘a’ litres removed from p and ‘a’ litres added from q
    So rate of vessel P after removal and then addition = [(160-a)p + aq]/160
    Similarly rate of vessel Q after removal and then addition = [(40-a)q + ap]/40
    Now equate these equations
    [(160-a)p + aq]/160 = [(40-a)q + ap]/40
    Solving, we get a = 32 l
  4. A book seller sold a book at Rs. 56 in such a way that his percentage profit is same as the cost price of the book. If he sells it at twice the percentage profit of its previous percentage profit then new selling price will be?
    A) Rs. 72
    B) Rs. 32
    C) Rs. 42
    D) Rs. 62
    E) None of these
    View Answer
    Option A
    Solution:
    CP = x
    SP = x + (x * x)/100 = 56
    x2 + 100x – 5600 = 0
    x = 40
    SP = 40 + (40 * 80)/100 = Rs. 72
  5. A circular road runs round a circular playground. If the difference between the circumferences of the outer circle and the inner circle is 132 metres, then what is the width of the road?
    A) 15 m
    B) 19 m
    C) 17 m
    D) 21 m
    E) None of these
    View Answer
    Option D
    Solution:
    Width of the Road = R – r
    2πR – 2πr = 132
    R – r = 132 * (7/44) = 21 m
  6. There are two concentric circles whose areas are in the ratio of 16:25 and the difference between their diameters is 8 m. Find out the area of the inner circle?
    A) 225πm2
    B) 256πm2
    C) 289πm2
    D) 144πm2
    E) None of these
    View Answer
    Option B
    Solution:
    r2/R2 = 25/16
    r/R = 5/4
    5x – 4x = 4
    x = 4
    Inner Radius = 16m
    Area of Inner Circle = Π (16 * 16) = 256πm2
  7. A boat takes 58 hours for travelling downstream from Point X to point Y and coming back to point Z midway between X and Y. If the speed of the stream is 4 kmph and speed of the boat in still water is 11 kmph, then what is the distance between X and Y?
    A) 520 km
    B) 370 km
    C) 480 km
    D) 420 km
    E) None of these
    View Answer
    Option D
    Solution:
    Speed downstream = 11 + 4 = 15 kmph.
    Speed upstream = 11 – 4 = 7 kmph.
    Let distance between P and Q be ‘x’ km, then,
    x/15 + (x/2)/7 = 58.
    i.e., x/15 + x/14 = 58.
    Solving we get, x = 420 km.
  8. A boat takes 4 hours more while going back in upstream than in downstream when the distance between two places is 32 km and the speed of boat in still water is 6kmph. What must be the speed of boat in still water so that it can row downstream, 32km in 4 hours?
    A) 6 kmph
    B) 8 kmph
    C) 4 kmph
    D) 4.5 kmph
    E) None of these
    View Answer
    Option A
    Solution:
    32/(6-R) – 32/(6+R) = 4
    R = 2kmph
    (B + 2) = 32/4
    Speed of boat in still water = 6kmph
  9. Ajay and Bala invest Rs. 4000 and Rs. 5000 in a business. Ajay receives Rs. 20 per month out of the profit as remuneration for running the business and the rest of profit is divided in proportion to the investment. In a year Ajay totally receives Rs. 672. What does Bala receives?
    A) Rs. 630
    B) Rs. 360
    C) Rs. 480
    D) Rs. 380
    E) Rs. 540
    View Answer
    Option E
    Solution:
    Annual profit = x
    Ratio of profit share between Ajay and Bala = 4 : 5
    Ajay gets: 20 * 12 + 4/9 * x = 672
    Solving, we get, x = 108*9
    So Bala gets = 5/9 * x = 5/9 * 108*9 = Rs 540
  10. Angel, Beaula and Catherine entered into a partnership in a business. Angel got 5/7 of the profit. Beaula and Catherine distributed the remaining profit equally. If Catherine got Rs.500 less than Angel, then the total profit was?
    A) Rs. 630
    B) Rs. 760
    C) Rs. 680
    D) Rs. 580
    E) Rs. 875
    View Answer
    Option E
    Solution:
    Total Profit = x
    Angel’s Share = (5x/7)
    Remaining Profit = x – (5x/7) = (2x/7)
    Beaula and Catherine distributed the remaining profit equally- x/7 , x/7
    (5x/7) -(1x/7)= 500
    (4x/7) = 500
    x = 500 * (7/4) = 875

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