Question

There are two vessels of milk of different prices with the
volume of 220L and 180L, respectively. Equal amounts of
milk were poured off simultaneously from the two vessels
and the milk poured off from the 1st vessel was poured into
the 2nd vessel and milk poured off from the 2nd vessel was
poured into the 1st vessel. Then the price of milk in both the
vessels becomes the same. How much milk was poured from
one vessel into the other?​

Answer 1

Given : two vessels of milk of different prices with the volume of 220L and 180L,

To find :   How much milk was poured from  one vessel into the other

Solution:

Let say Price per litre of 220L  is  A per Litre

Hence total cost of Vessel 220L = 220A

Let say Price per litre of 180L  is  B per Litre

Hence total cost of Vessel 180L = 180B

Let say L  Litre  moved  from each vessel

Price  220 L vessel

=  ((220 - L ) A  +  L B ) / 220

Price of 180 L vessel

= ((180 - L)B  + L A ) /180

( (220 - L ) A  +  L B ) / 11   = ((180 - L)B  + L A ) /9

=> 9A(220 - L) + 9LB = 11B(180 - L)  + 11LA

=> 1980A - 9LA + 9LB = 1980B - 11BL  + 11LA

=> 1980(A - B ) = 20LA - 20LB

=> 1980 (A - B) = 20L(A - B)

=> 20L = 1980

=> L = 99

99 litre milk was poured from one vessel into the other

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