Quant Boosters by VP - Set 2



  • For each seat there is 1 win and 3 losses
    so total no of losses = 87 means no of seats = 87/3 = 29



  • Q15) Contractor undertakes to dig 10km long canal in 180 days and employs 40 men. After 60 days they finished only 2.5km of canal. To complete the wirk on time, how much more men needs to be hired?



  • Work done = 2.5 left=7.5 (3 times)
    time = 60 days left=120 days(2 times)
    so to do 3 times work in 2 times time, need 3/2 times men
    3*40/2 = 60 men
    so 6-40=20 more men needs to be hired.



  • Q16) There are 3 runners Aman, Badal and Carol. Aman beats Badal by 20m amd Carol by 34m. Badal beats Carol by 21m. Find length of race.



  • While Badal travelled 20m, Carol travelled 34-21=13m
    so speed ratio B:C=20:13
    so B/C = 20/13 = (L-20)/(L-34)
    L=60m



  • Q17) I wanted to buy 2 dozen bananas but I am 30 Rupees short. So I bought 20 bananas and 2 rupees is left with me. Price of 1 banana?



  • 24 bananas cost= > 30 more than what I have
    20 bananas cost = > 2 less than what I have
    So 4 bananas cost 30+2=32rupees
    1 banana cost 8 rupees



  • Q18) 100 kg grapes contains 98% water. After few days, due to evaporation some water evaporates and it contains 94% of water. Find weight of grapes.



  • 98% water means 2% mass=2kg mass
    When water evaporates, water=94% so mass =6%
    but mass is constant so 2 kg = 6%
    Numerator(mass) is same but fraction increased 3 times. So denominator decreased 3 times
    100/3 = 33.33 kg new weight of grapes.



  • Q19) If 8 coins are tossed, what is the probability that no two heads appear consecutively.



  • Use Fibonacci function
    F(0) = 1
    F(1) = 2
    F(2) = 1 + 2 = 3
    F(3) = 2 + 3 = 5
    F(4) = 3 + 5 = 8
    F(5) = 5 + 8 = 13
    F(6) = 8 + 13 = 21
    F(7) = 13 + 21 = 34
    F(8) = 21 + 34 = 55

    So 55/2^8 Ans

    It's like 3 coins ho tab find f(3)
    4 coins ho tab f(4)
    N coins k liye f(n) that's generalisation
    Example try for 3 coins
    hhh
    hht
    hth
    htt
    thh
    tht
    tth
    ttt
    5/8 Hai

    Or directly f(3)/2^8 = 5/8



  • Q20) There were x pigeons and y mynahs in a cage. One fine morning p of them escaped to freedom. If the bird keeper, knowing only that p = 7, was able to figure out without looking into the cage that at least one pigeon had escaped, then which of the following does not represent a possible (x,y) pair?
    a) (10, 8)
    b) (7, 2)
    c) (25, 6)
    d) (12, 4)



  • For the bird keeper to figure out that at least 1 pigeon had escaped, the number of mynahs has to be less than 7. In other words, y < 7. Hence, the pair (10,8) is not a valid one.



  • Q21) Anuj likes to jog in a park. While jogging he also calculates his speed and the number of steps taken by him. He observes that the steps taken by him per minute are 5 times his speed in km/hr. What is the distance he covers per step if he jogs at a uniform speed ?



  • let x km per hr be the speed
    so 5x steps per min = 5x * 60 = 300x steps per hour
    so 300x steps = x km
    300x steps = 1000x m
    1 step = 10/3 m ?



  • Q22) The probability of a car passing a certain intersection in a 20 minute windows is 0.9. What is the probability of a car passing the intersection in a 5 minute window? (Assuming a constant probability throughout)



  • Probability of a car passing in a 20 minute window = 1 – (probability of no car passing in a 20 minute window)
    Probability of a car passing in a 20 minute window = 1 – (1 – probability of a car passing in a 5 minute window)^4
    0.9 = 1 – (1 – x)^4
    (1 – x)^4 = 0.1
    1 - x = .1^.25
    x = 1 - .1^.25



  • Q23) When three brands of juices are mixed in the ratio of 3 : 4 : 5 and 4 : 5 : 6, the cost price of the mixture of these two juices comes out to be Rs. 20 and Rs. 25 per litre respectively. Find the cost price of a litre of mixture of juices in which the three brands are mixed in the ratio of 6 : 7 : 8.



  • (3x + 4y + 5z)/(3 + 4 + 5) = 20
    => 3x + 4y + 5z = 20 * 12 ----- (1)
    (4x + 5y + 6z)/(4 + 5 + 6) = 25
    4x + 5y + 6z = 25 * 15.....(2)
    6x + 7y + 8z=?
    3 * (2) - 2 * (1)
    => 6x + 7y + 8z = 3 * 25 * 15 - 2 * 20 * 12
    =645
    per litre cost
    = 645/(6+7+8)
    =645/21
    = 215/7



  • Q24) A Contractor employed a certain number of workers to finish constructing a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the scheduled time, so he at once doubled the no of workers and thus he managed to finish the road on the scheduled time. How much work he had been completed, before increasing the number of workers?


 

Looks like your connection to MBAtious was lost, please wait while we try to reconnect.