If X beakers of 100ml containing 1:4 acid-water solution are mixed with Y beakers of 200ml containing 3:17 acid-water solution then the ratio of acid to water in the resulting mixture becomes 19:91. Find X:Y.
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Answer:
x : y = 5 : 3
Step-by-step explanation:
beakers of 100 ml containing 1 : 4 acid-water solution
=> acid = 100 * 1/5 = 20 ml
Water = 100 * 4/5 = 80 ml
in x beaker acid = 20x ml
& in x beakers water = 80x ml
beakers of 200 ml containing 3 : 17 acid-water solution
=> acid = 200 * 3/20 = 30 ml
& water = 200 * 17/20 = 170 ml
in y beaker acid = 30y ml
& in y beakers water = 170y ml
Acid = 20x + 30y
Water = 80x + 170y
Resulting mixture = 19 : 91
=> (20x + 30y)/( 80x + 170y) = 19/91
=> (2x + 3y) /(8x + 17y) = 19/91
=> 91(2x + 3y) = 19(8x + 17y)
=> 182x + 273y = 152x + 323y
=> 30x = 50y
=> 3x = 5y
=> x /y = 5/3
=> x : y = 5 : 3
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