Quant Boosters - Vikas Saini - Set 1



  • Suppose he sold x no of rings at profit of 15%.
    (361-x)x(1-4/100)+x (1+15/100) = 361 x (1+8/100)
    361 x 0.96 – 0.96x + 1.15x = 361x1.08
    0.19 x = 361(1.08-0.96)
    X = 361 x (0.12) / (0.19) = 228.

    Short approach :-
    By allegation

    -4 -- 15

    -- 8 --

    7 -- 12

    No of rings = [(12)/(12+7)] x 361 = 228.



  • Q16) On selling 17 balls at rs 720, there is loss equal to the cost price of 5 balls.The cost price of a ball is
    a. 45 rs
    b. 50rs
    c. 55rs
    d .60 rs.



  • Short approach :-
    Cp of ball = selling price of all balls / (total balls – loss(no of balls)
    = 720 / (17-5 )
    = 60 rs.



  • Q17) A, B and C start simultaneously from X to Y. A reaches Y, turns back and meet B at a distance of 11 km from Y. B reached Y, turns back and meet C at a distance of 9 km from Y. If the ratio of the speeds of A and C is 3:2, what is the distance between X and Y?



  • Suppose distance between X and Y is D km.
    A = D+11, B = D-11.
    B = D+9, C = D-9.
    A/C = 3:2.
    (AB) / (BC) = 3/2.
    (D+11) (D+9) / (D-11) (D-9) = 3 / 2.
    D^2 + 20D + 99 / D^2 – 20D + 99 = 3 / 2
    2(D^2 + 20D + 99) = 3(D^2 – 20 D + 99)
    D^2 – 100 D + 99 = 0.
    D = 99.



  • Q18) A shopkeeper uses a weight of of 460 gm instead of 500 gm and sells the article at the cost price. What is profit percentage ?
    a. 40%
    b. 23%
    c. 8 +16/23 %
    d. 20%



  • Short approach :
    Profit percentage = [ (500 – 460)/460] x 100
    = (40/460) x 100



  • Q19) A 30% solution of alcohol is mixed with a 50% solution of alcohol to form a 10 litre solution of 45% alcohol. How much of 30% solution was used.
    (a) 2 ltr
    (b) 2.5 ltr
    (c) 2.7 ltr
    (d) 3.2 ltr
    (e) 3.7 ltr



  • By allegation
    30 --- 50
    -- 45 --
    (50-45 ) : (45-30)
    5 : 15 = 1 : 3.
    Ratio = 1 : 3
    30% solution was added = 10 x 1 / (1 + 3) = 2.5 ltr.



  • Q20) The percentage volumes of milk in three solutions A,B and C form a geometric progression in that order. If we mix the first, second and third solutions in the ratio 2:3:4, by volume we obtain solution containing 32% milk. If we mix them in the ratio 3:2:1, by volume, we obtain a solution containing 22% milk. What is the percentage of milk in A?
    a) 6%
    b) 12%
    c) 18%
    d) 24%



  • Suppose volumes of milk percentage in A,B,C are a, ar, ar^2 respectively.
    2a + 3ar + 4ar^2 = 32 x 9.
    3a + 2ar + ar^2 = 22 X 6.
    a= 12, r = 2.
    The percentage of milk in A = 12%.



  • Q21) One fourth of a solution that was 10% sugar by weight was replaced by a second solution resulting in a solution that was 16% sugar by weight. The second solution was what percent sugar by weight ?



  • 10 -- X
    -- 16 --
    X-16 : 16 - 10
    1 : 1/3
    X – 16 / 6 = 3 / 1
    X = 34.



  • Q22) From a solution that has milk and water in the ratio 5 : 3, ‘x’ percent is removed and replaced with water. The concentration of milk in the resulting solution lies between 30% and 50%. Which of the following best describes the value of ‘x’?
    a) 25 < x < 30
    b) 20 < x < 52
    c) 20 < x < 48
    d) 25 < x < 60



  • Suppose total unit is 8. Milk = 5, water = 3.
    X% of 8 is removed = 0.08x.
    Where milk part is 0.05x and water part is 0.03x.
    0.30 < 5 – 0.05x / 8 < 0.50
    2.40 < 5 – 0.05 x < 4.0
    -2.60 < -0.05x < -1.
    1 < 0.05x < 2.6
    20 < x < 52.
    Option B



  • Q23) The concentration of milk in 60L milk and water solution is 30%. If 6L of the solution is replaced by water then 5L solution is again replaced by water, then find the concentration of milk in the final solution.
    a) 24.50 %
    b) 25.00%
    c) 24.75 %
    d) 25.50%



  • The concentration in final solution = (3/10) ( 1 - 6/60) (1 – 5/60)
    = 24.75%.



  • Q24) Rice of two different qualities are mixed and the mixture is sold at rs. X per kg, giving 25% profit. If higher quality rice is sold at rs X per kg, then there will be a loss of 100/11 %. If the ratio of the quantities of the lower quality rice and the higher quality rice in the mixture is 8 : 3, then what is the percentage profit when lower quality rice is sold at X per/kg ?



  • Cost price of low quality rice per kg is l and cost price of high quality rice per kg is h.
    (8l + 3h / 11)(5/4) = h (10/11)
    8l = 5h.
    Cost price of lower quality rice is 5h/8.
    Selling price of mixture = 10h/11.
    Profit percentage = (10h/11 – 5h/8) x 100 / (5h/8) = 500/11 %.



  • Q25) Two containers X and Y, equal quantities of water and acid. The concentration of acid is same in both the containers X and Y. If 4 litres of solution from X is replaced by acid and the concentration of acid becomes twice what it was initially. If 8 litres of solution is from Y is replaced with pure acid then what is the ratio of final concentration of acid in solution Y to the initial concentration of acid in solution Y ?


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