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Mixture and Alligation #23

23. We have a 630 ml mixture of milk and water in the ratio 7:2. How much water must be added to make the ratio 7:3?
A. 60 mlB. 70 ml
C. 50 mlD. 80 ml

Answer: Option B

Explanation:

concentration of water in mixture1 $=\dfrac{2}{9}$ (since the ratio of milk and water = 7:2) ...(1)

concentration of water in pure water= 1 ...(2)

Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3
=> concentration of water in mixture2 $=\dfrac{3}{10}$

By rule of alligation,

concentration of water in mixture1 $\left(\dfrac{2}{9}\right)$concentration of water in pure water (1)
Mean concentration
$\left(\dfrac{3}{10}\right)$
$1-\dfrac{3}{10}=\dfrac{7}{10}$$\dfrac{3}{10}-\dfrac{2}{9}=\dfrac{7}{90}$

=> Quantity of mixture1 : Quantity of water
$=\dfrac{7}{10}:\dfrac{7}{90}=\dfrac{1}{10}:\dfrac{1}{90}=1:\dfrac{1}{9}$

Given that Quantity of mixture1 = 630 ml
=> 630 : Quantity of water $=1:\dfrac{1}{9}$
=> Quantity of water $=630 ×\dfrac{1}{9}=70$ ml

Comments(1)

profileM.Suresh
2016-08-25 09:30:13 
Let water + milk = 630 ml

from the question M:W=7:2. So,
water quantity = 2/9 * 630 = 140
milk quantity =630-140=490,

then,
490/(140+x)=7/3
=> 1470-980=7x
=> x=490/7 = 70
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