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In a 729 litres mixture of milk and water, the ratio of milk to water is 7 : 2. to get a new mixture containing milk and water in the ratio 7 : 3, the amount of water to be added is:

A. 81 litres

B. 71 litres

C. 56 litres

D. 50 litres

Answer: Option A

Solution(By Examveda Team)

Quantity of milk in 729 litre of mixture
= 7 × $$\frac{{729}}{{9}}$$ = 567 litre
Quantity of water
= 729 - 567
= 162 litres
Let x litre of water be added to become ratio 7 : 3
Alligation mcq Solution 2
Or, $$\frac{{7}}{{3}}$$ = $$\frac{{567}}{{162 + {\text{x}}}}$$
Or, 162 × 7 + 7x = 567 × 3
Or, 7x = 1701 - 1134 = 567
Or, x = $$\frac{{567}}{{7}}$$ = 81 litres water is to be added.

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Comments ( 9 )

  1. Rasmita Sahoo
    Rasmita Sahoo :
    1 year ago

    (Real/ratio)×added
    ={729/(7+2)}×(3-2)
    =(729/9)×1
    =81

  2. Himanshu Das
    Himanshu Das :
    1 year ago

    7x+2x=9x
    9x=729

    2X=162
    162+x/576=3/7
    X=81

  3. Abir Mahmud
    Abir Mahmud :
    2 years ago

    Milk : Water = 7 : 2
    Milk : Water = 7 : 3
    Now, (7 + 2) i.e 9 units ≡ 729 L
    So, (3 - 2) i.e 1 units ≡ 81L (Ans.)

  4. Md Maruf
    Md Maruf :
    2 years ago

    1st term 7:2 = 9
    2nd term = 7:3 where only water difference 3-2 = 1
    now
    9x = 729
    or x = 81

  5. Md Helal
    Md Helal :
    4 years ago

    Qty of Milk = 729*(7/9) = 567 L
    Qty of Water = 162 L
    Had to mix water (3 - 2 ) = 1 unit
    ATQ, 7 ≡ 567
    Then, 1 ≡ (567/7) = 81 L

  6. MAHENDRA SINGH
    MAHENDRA SINGH :
    5 years ago

    lets 1 part to be mixed so as per allegation method take only same qty ratio
    so i am taking water ration
    2/9 : 1(assume 1 part water to be mixed)
    3/10
    (1-3/10=7/10) (3/10-2/9= 7/90)
    so ratio is 7/10 : 7/90 = 9:1
    now water to be added 1/9 x729 = 81 litres


  7. Reejo Paul
    Reejo Paul :
    6 years ago

    How about just taking 1 part of the ratio 7:2 which amounts to 81 litres. (1/9 of 729 = 81). Since 7:2 changes to 7:3. only 1 part of water is increasing.

  8. Surbhi Deshwal
    Surbhi Deshwal :
    6 years ago

    Let 729=X
    a:b = 7:2
    c:d =7:3

    formula : Water added=X(ad-bc)/c(a+b)
    ans 81

  9. Srinivas Jami
    Srinivas Jami :
    7 years ago

    if the raito was 7:2,then we r calculating as 7*729/2.Then as the same way for 7:3 we can calculate
    Quantity of milk in 729 litre of mixture
    7*729/10 =510.3
    Quantity of water needed
    729-510.3=218.7
    As by 7:2 ratio the water was 162 litres.
    Now by subtracting 162 from 218.7 ans comes
    218.7-162=56.7
    As the most appropriate ans is 56

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