IBPS Clerk Prelims: Quants Day 21

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Stratus – IBPS Clerk Course 2015 

Stratus - IBPS Clerk - Daily Test - Quants
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  1. The speed of a boat in still water is 36 km/h. If the boat goes 56 km upstream in 1 hour 45 minutes, what is the time taken by the boat to cover the same distance down the stream?
    A) 2 hours 25 minutes
    B) 3 hours
    C) 1 hour 24 minutes
    D) 2 hours 21 minutes
    E) 2 hours
    Answer & Explanation
    C) 1 hour 24 minutes
    Explanation:

    Speed of boat in still water (B) = 36 km/hr
    1hr 45 min = 1 + 45/60 = 7/4 hrs
    Upstream speed (U)= 56/(7/4) = 32 km/hr
    B = (D+U)/2, so 36 = (D+32)/2, D = 40 km/hr
    Time for downstream = 56/40 = 7/5 hrs = 1 2/5 hrs = 1 hr 2/5 * 60 mins = 1 hr 24 mins
  2. The speeds of A and B are in the ratio of 3 : 4 when they cover same distance. In this journey, A takes 30 minutes more than B to reach their destination. Find the time taken by A to reach the destination.
    A) 3 minutes
    B) 1/2 hour
    C) 1 1/2 hours
    D) 2 hours
    E) 3 1/2 hours
    Answer & Explanation
    D) 2 hours
    Explanation:

    Speed of A = 3x, speed of B = 4x
    Difference in time to reach destination is 30 min or 1/2 hour
    Total distance = ((3x*4x)/(4x – 3x)) * 1/2 = 6x
    Time taken by A to travel 6x = 6x/3x = 2 hrs
  3. An alloy contains 2 metals. The first alloy weighs 5 kg in which 1st metal is 1/3rd and the rest is 2nd metal. The second alloy weighs 2 kg in which 1st metal is 1/4th and the rest is 2nd metal. If both alloys are mixed, find the ratio of the weights of 1st metal to 2nd metal in the final mixture?
    A) 13 : 19
    B) 13 : 29
    C) 20 : 41
    D) 19 : 29
    E) None of these
    Answer & Explanation
    B) 13 : 29
    Explanation:

    2nd metal in first alloy = 1 – 1/3 = 2/3
    2nd metal in second alloy = 1 – 1/4 = 3/4
    New ratio = (1/3 * 5 + 1/4 * 2) : (2/3 * 5 + 3/4 * 2)
  4. A completes a piece of work in the same time in which B and C can together do the work. If A and B together complete the work in 10 days and C alone does the work in 50 days, then B alone could do the same work in:
    A) 20 days
    B) 22 days
    C) 25 days
    D) 28 days
    E) None of these
    Answer & Explanation
    C) 25 days
    Explanation:

    (A+B+C)’s 1 day’s work: 1/A + 1/B + 1/C = 1/10 + 1/50 = 3/25
    Given 1/A = 1/B +1/C
    So, 1/A +1/A = 3/25 gives 1/A = 3/50
    1/A + 1/B = 1/10, so 1/B = 1/10 – 3/50 = 1/25
    So B can do in 25 days
  5. The circumference of the base of a right circular cylinder is 66 cm and curved surface area of the cylinder is 2640 cm2. Find the volume of this cylinder.
    A) 8205 cm3
    B) 13960 cm3
    C) 9680 cm3
    D) 14480 cm3
    E) None of these
    Answer & Explanation
    C) 13860 cm3
    Explanation:

    2ᴨr = 66
    2ᴨrh = 2640
    Find r and h.
    Volume = ᴨr2h
  6. A dealer marked an article at 60% above the cost price. At the time of selling he offered a discount of 20% so as to have a profit of 40% on the article. What is his actual profit percent?
    A) 25%
    B) 16 2/3%
    C) 28%
    D) 13 1/3%
    E) 18%
    Answer & Explanation
    C) 28%
    Explanation:

    The actual profit% will be 60 – 20 + (60)(-20)/100
  7. 12 children can complete a piece of work in 16 days and 8 adults complete the same work in 12 days. 16 adults start the work and after 3 days, 10 of the adults left and in place of them 4 children joined. In how many days the remaining work will be completed?
    A) 10 days
    B) 3 days
    C) 4 days
    D) 8 days
    E) 6 days
    Answer & Explanation
    E) 6 days
    Explanation:

    12 c in 16 days, so 1 child in 12*16 days. So 4 children in 12*16/4 = 48 days
    8 a in 12 days, so 1 adult in 8*12 days. 16 adults in 8*12/16 = 6 days
    16 adults worked for 3 days, so in 3 days they do 1/6 * 3 = 1/2 work
    10 adults left, 6 left, 6 adults do in 8*12/6 = 16 days
    So 6 adults and 4 children’s 1 day work = 1/16 + 1/48 = 1/12. Let they complete remaining work (1 – 1/2 = 1/2) in x days
    So 1/12 * x = 1/2
    x = 6
  8. Some men are employed to complete a piece of work in 60 days. But if 8 more men are employed then the same work could be completed in 10 days less. Find the number of men initially employed.
    A) 40 men
    B) 42 men
    C) 48 men
    D) 38 men
    E) 32 men
    Answer & Explanation
    A) 40 men
    Explanation:

    Let number of men = x.
    8 more men means x + 8, 10 days less means (60 – 10) = 50 days. Then,
    M1 * D1 = M2 * D2
    x*60 = (x + 8)*50
    x = 40 men
  9. 8x2 + 6x = 5, 12y2 – 22y + 8 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relationship cannot be determined
    Answer & Explanation
    (D) x ≤ y
    Explanation:

    8x2 + 6x – 5 = 0
    8x2 + 10x – 4x – 5 = 0
    2x(4x+5) – (4x+5) = 0
    x = 1/2 , -5/4
    12y2 – 22y + 8 = 0
    12y2 – 16y – 6y +8 = 0
    4y(3y-4) – 2(3y-4) = 0
    y = 1/2, 4/3
    put on number line
    -5/4 1/2 4/3
  10. 7x + 16y = 75, 6x – 8y = -9
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relationship cannot be determined
    Answer & Explanation
    (B) x < y
    Explanation:

    To solve the equations, multiply 2nd equation by 2, and add both equations:
    7x + 16y = 75
    12x – 16y = -18
    On addition – 19x + 0y = 75-18
    Or 19x = 57
    x = 3
    now put x=3 in any of the equations to find y, y= 27/8