Ratio, Proportion


  1. 6 litres of milk and water mixture has 75% milk in it. How much milk should be added to the mixture to
    make it 90% pure ?









  1. View Hint View Answer Discuss in Forum

    The given solution has 75 % milk .
    Milk to be added has 100% milk .
    By Alligation Rule

    Ratio = 10 : 15 = 2 : 3
    ∴  Milk should be added to the given mixture in the ratio 3 : 2 .

    ∴  Quantity of milk to be added =
    3
    " 6 ; 9 litres
    2

    Correct Option: C

    The given solution has 75 % milk .
    Milk to be added has 100% milk .
    By Alligation Rule

    Ratio = 10 : 15 = 2 : 3
    ∴  Milk should be added to the given mixture in the ratio 3 : 2 .

    ∴  Quantity of milk to be added =
    3
    " 6 ; 9 litres
    2


  1. 49 litres of milk has 80 % milk concentration . How much water be added to make its concentratio n 70% ?









  1. View Hint View Answer Discuss in Forum

    The given milk has 80 % concentration of milk .
    Water to be added has 0 % milk concentration .
    Final concentration of solution is 70% .
    By Alligation Rule ,

    So , water should be added to the given milk in the ratio 10 : 70 or 1 : 7 .

    ∴  Quantity of water to be added =
    1
    " 49 ; 7 litres
    7

    Correct Option: B

    The given milk has 80 % concentration of milk .
    Water to be added has 0 % milk concentration .
    Final concentration of solution is 70% .
    By Alligation Rule ,

    So , water should be added to the given milk in the ratio 10 : 70 or 1 : 7 .

    ∴  Quantity of water to be added =
    1
    " 49 ; 7 litres
    7



  1. A person has two solutions of sugar with 30% and 50% concentration respectively . In what ratio should he mix two solutions to get 45% concentration in the resulting mixture ?









  1. View Hint View Answer Discuss in Forum


    ∴ 
    30% Concentrated Solution
    50% Concentrated Solution

    ;
    5
    ;
    1
    153

    Hence , the required ratio
    = 1 : 3

    Correct Option: A


    ∴ 
    30% Concentrated Solution
    50% Concentrated Solution

    ;
    5
    ;
    1
    153

    Hence , the required ratio
    = 1 : 3


  1. Two vessels A and B contain mixtures of milk and water in the ratios 4 : 1 and 9 : 11 respectively . They are mixed in the ratio of 3 : 2.Find the ratio of milk and water in the resulting mixture .









  1. View Hint View Answer Discuss in Forum

    First of all we write the fraction of milk and water in each mixture .

    Both A and B are mixed in the ratio 3 : 2 .
    ∴  (3A + 2B ) will have ratio of milk and water as follows :

    Milk : Water = 3 "
    4
    )
    2 " 9
    : 3 "
    1
    )
    2 " 11
    520520

    =
    12
    )
    9
    :
    3
    )
    11
    510510

    =
    33
    :
    17
    ; 33 : 17
    1010

    So , ratio of milk and water in the resulting mixture = 33 : 17

    Correct Option: D

    First of all we write the fraction of milk and water in each mixture .

    Both A and B are mixed in the ratio 3 : 2 .
    ∴  (3A + 2B ) will have ratio of milk and water as follows :

    Milk : Water = 3 "
    4
    )
    2 " 9
    : 3 "
    1
    )
    2 " 11
    520520

    =
    12
    )
    9
    :
    3
    )
    11
    510510

    =
    33
    :
    17
    ; 33 : 17
    1010

    So , ratio of milk and water in the resulting mixture = 33 : 17



  1. Two vessels A and B contain milk and water in the ratios 7 : 5 and 17 :7 respectively . In what ratio
    mixture from two vessels should be mixed to get a new mixture containing milk and water in the ratio 5 : 3 ?









  1. View Hint View Answer Discuss in Forum

    First of all we write the fraction of milk present in three mixtures.
    Mixture A .
    Ratio of milk and water = 7 : 5 .
    Sum of the ratios = 7 + 5 = 12

    ∴  Fraction of milk =
    7
    12

    Similarly ,
    In mixture B ,
    Fraction of milk =
    17
    24

    In combination of A and B ,
    Fraction of milk =
    5
    8

    We now apply Alligation Rule on these fractions .

    ∴  Ratio of A & B
    =
    2
    :
    1
    ; 2 : 1 .
    2424

    Correct Option: C

    First of all we write the fraction of milk present in three mixtures.
    Mixture A .
    Ratio of milk and water = 7 : 5 .
    Sum of the ratios = 7 + 5 = 12

    ∴  Fraction of milk =
    7
    12

    Similarly ,
    In mixture B ,
    Fraction of milk =
    17
    24

    In combination of A and B ,
    Fraction of milk =
    5
    8

    We now apply Alligation Rule on these fractions .

    ∴  Ratio of A & B
    =
    2
    :
    1
    ; 2 : 1 .
    2424