Alligations or Mixtures
Aptitude

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Q.

How much water must be added to 60 litres of milk at 1.5 litres  for Rs. 20 So as to have a mixture worth Rs.$10\dfrac{2}{3}$ a litre?

 A.

10 litres

 B.

12 litres

 C.

15 litres

 D.

18 litres

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Solution:
Option(C) is correct

C.P. of $1.5=\dfrac{3}{2}$ litre of milk = Rs. 20

C.P. of 1 litre of milk = Rs. $\dfrac{20 \times 2}{3}$ = Rs. $\dfrac{40}{3}$

C.P. of 1 litre of water $= 0$

From question,

Mean price Rs.$10\dfrac{2}{3}$

= Rs. $\dfrac{32}{3}$

By the rule of alligation, we have:

C.P of 1 litre        C.P of 1 litre

   of water               of milk

     (0)                  $\left(Rs. \dfrac{40}{3}\right)$

             \                /
            Mean Price

              $\left(Rs. \dfrac{32}{3}\right)$

             /               \

  $\left(\dfrac{40}{3}-\dfrac{32}{3}\right)$    $\left(\dfrac{32}{3-0}\right)$

         $=\dfrac{8}{3}$              $=\dfrac{32}{3}$

Ratio of water and milk $=\dfrac{8}{3}:\dfrac{32}{3}$

$=8:32=1:4$

Thus, Quantity of water to be added to 60 litres of milk: (Note it is extra water that is to be added and final solution is not of 60 litre but more than that).

$\left(\dfrac{1}{4}\times 60\right)$ litres

$=15$ litres

Note: Based on the comment from abhishek final answer is modified and final ans is changed from 15 litre to 12 litre.

Edit2: As tharun points out in the comment, it was asked that how many litres of water is added to 60 litre milk that means total quantity after addition of water should be grater than 60. So total volume AFTER addition of water should be 75 and the quantity of water added is 15 litre.


(19) Comment(s)


Rajesh Kumar
 ()

dont confuse .water to be added x .. x/60 = 1/4

x=15 litres



Manpreet Kaur
 ()

The solution is correct

See, water and milk are in 1:4 ratio. If milk is 60 lts.

So, 4 parts = 60 lt

1 Part $=\dfrac{60}{4}$

As some are saying $\dfrac{60}{5}$

Tt would be the case if the total mixture is given.

So $\dfrac{60}{4}=15 \textbf{ litre}$ is the correct answer.


Charu
 ()

those who have confusion can do like this take the added quantity of water x

ratio is 1:4

1/5=x/x+60

where x+60 is the total volume and 5 is the total volume in parts

therefore the solution is correct


Tharun
 ()

In the question it was asked as how many litres of water is added to 60 litre milk that means total quantity after addition of water should be grater than 60. But here in the ans total volume is considered as 60.

I think total volume after addition of water should be 75 and the quantity of water added is 15 litre


Deepak
 ()

You have correctly pointed out the error in the modified solution. Changed the solution accordingly. Thank you for keeping us on track.


Debayan
 ()

I have a confusion with the solution that how do the mean price come 32/3??


Sujeet
 ()

Because it is mentioned in the question.


Abhishek
 ()

Ratio came out to be $1:4$ therefore water should be $\left(\dfrac{1}{5} \times 60 \right)=12$. So option B should be correct.


Deepak
 ()

Thank you for pointing out, corrected the final answer.

Sidharth
 ()

60 is not the total amount, it is the milk quantity added into the water

Therefore, you can write it down like quantity of water :quantity of milk=1:4(proved above) , given 60 liter the quantity of milk.

W:60=1:4, from this you can find out the quantity of water.

correct answer is 15.

Akhilesh
 ()

wrong answer should be 15 liter.

water:milk=1:4

water:60=1:4

to make ratio 1:4 water should be 15 L.

so Abhishek 1/5*(mixture)=1/5*75


Vidhya
 ()

for 1.5 litre i.e $1 \dfrac{1}{2} =20$ rs

for 1litre = ?

so $\dfrac{20}{3/2} =\dfrac{20\times 2}{3}$

thus $

dfrac{40}{3}$



Vimal
 ()

MEAN PRICE - calculation ??

Somebody pls explain the calcution of M.P.

I guess of 3/2 L is for Rs.20

then 1L is for 20x2/3=40/3

then , 2/3 L for Rs 10

gives 1 L for 10x3/2 = 15 (pls explain how you got got/get 32/3)

(* Sunny's magical math went above my head )

BTW ,the later part should be..

Qty of Water = 1/5*60 litre

= 12 litres

pls help



Sunny
 ()

\(10 \dfrac{2}{3} = \dfrac{(10*3)+2}{3} =\dfrac{32}{3}\)



Sunny
 ()

its given as:



Chandan Singh
 ()

I am confused in mean price. How did you find in this problem ?



Selvakumar
 ()

mean price kaise nikala ?



Archita
 ()

how did u do dis..Thus, Quantity of water to be added to 60 litres of milk,

$=\dfrac{1}{4} \times 60$

quantity of water shud be $= \dfrac{\text{water}}{\text{total}} \times 60$



Pragya Shiva
 ()

mean price kaise nikala ?