Ratio and Proportion - Price remain same

Question :-
There are two qualities of milk - Amul and Sudha having different prices per litre, their volumes being 130 litres and 180 litres respectively. After equal amounts of milk was removed from both, the milk removed from Amul was added to Sudha and viseversa. The resulting two types of milk now have the same price. Find the amount of milk drawn out from each type of milk.


Solution : Key point here is the price of mixture (Price per litres) remain same after mixing.

Assume 130 has P is price per liters and 180 has Q is price per liters.

Let X is subtracted from both of them so price per litre can be given as :-

=> {(130-X)P + XQ}/130 = {(180-X)Q + XP}/180
=> (1-X/130)P + XQ/130=(1-X/180)Q + XP/180
=> P- XP/130 +XQ/130 = Q-XQ/180 + XP/180
 => P-Q - X/130 (P-Q) = X/180(P-Q)
Assume P-Q as K, we can do this because its given P and Q are different. This K gets cancel out from equation.
=> K-X/130(K) = X/180(K)
=> 1-X/130=X/180
=> 1 = X/130 + X/180
All question of these type will most certainly come to this point, so its better if you keep this formula in mind to speed up calculation.

Finally we get the value of X as,

X=75.48 liters

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