A solution contain wine and water in ratio 2:1 Out of it 36 litre solution is replaced by 15 litre water. Again 26 litre solution is replaced by same quality of water. Now wine water ratio become 8:7 Find difference between water quantity in initial and final solution.
Answers
Given : A solution contain wine and water in ratio 2:1 Out of it 36 litre solution is replaced by 15 litre water. Again 26 litre solution is replaced by same quality of water. Now wine water ratio become 8:7
To find : difference between water quantity in initial and final solution.
Solution:
Let Say
Wine = 2A Litre
Water = A Litre
Total Solution = 3A Litre
36 litre solution is replaced by 15 litre water.
=> Wine = 2A - (2/3)36 = 2A - 24 Litre
Water = A - (1/3)36 = A - 12 + 15 = A + 3 Litre
Wine = 2(A - 12)
Water = A + 3
=> Total = 3A - 21 = 3(A - 7)
now 26 litre Solution is replaced by water
Wine = 2(A - 12) - 26*2(A - 12)/3(A - 7) = (6A² -114A + 504 -52A + 624)/3(A - 7)
=> Water = A + 3 - 26(A + 3)/3(A - 7) + 26 = (3A² + 66A - 609 -26A - 78)/3(A - 7)
=> (6A² -166A + 1128)/( (3A² + 40A - 687) = 8/7
=> (3A² -83A + 564)/( (3A² + 40A - 687) = 4/7
=> 21A² - 581A + 3948 = 12A² + 160A - 2748
=> 9A² - 741A + 6696 = 0
=> 3A² - 247A + 2232 =0
=> 3A² - 216A - 31A + 2232 =0
=> 3A(A - 72) -31(A - 72) = 0
=> (3A - 31) (A - 72) = 0
=> A = 31/3 or A = 72
A = 31/3 not possible as then totaol solution initially = 31 litre while 36 litre taken out
Hence
A = 72
Water in initial = 72
Water in Final = A + 3 - 26(A + 3)/3(A - 7) + 26 putting A = 72 = 91
Water in Final = 91
Difference = 91 - 72 = 19
difference between water quantity in initial and final solution. = 19 Litre
Wine Water Total
144 72 216
120 75 195
104 91 195
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