Question

A solution contains milk:water = 9:2. 11 lit of this Sol is taken out & 5 lit of water is added. Again 16lit of Sol is taken out & replaced by water. If the final ratio of m:w = 9:13. Find the initial quantity of the solution?

Answer 1

Answer:

43.77 litre

Step-by-step explanation:

let say initial quantity of solution= 11S litre

milk =.9S litre

water = 2S litre

11 litre solution is take out and 5 litre water added

so now milk.= 9S - 9

water = 2S - 2 + 5 = 2S + 3

now ratio of milk and water

= 9(S-1): (2S +3)

total solution 11S - 6

now 16 litre is removed and 16 litre water is added

Milk removed =((9S-9)/(11S-6) )×16

water removed =( (2S +3)/(11S -6) )×16

now milk = (9S -9 )( 1 - 16/(11S-6))

= 9(S-9)(11S -22)/(11S-6)

= 99(S-1)(S-2) /(11S-6)

=(9)(11S^2 - 33S + 22)/(11S-6)

water =(2S+3)(1 - 16/(11S-6)) + 16

= (2S+3)(11S -22)/(11S -6) + 16

= ((22S^2 -11S -66) + (176S - 96))/(11S-6)

=( 22S^2 + 165S - 162)/(11S- 6)

ratio 9:13

13((11S^2 - 33S + 22) = 22S^2 + 165S - 162

143S^2 - 429S + 286 = 22S^2 + 165S - 162

121S^2 - 594S + 448 =.0

on solving S = 3.977 or less than 1

11S = 43.77 L