a jar contains a mixture of syrup A and B in the ratio 3:2. The volume of contents is increased by 50% by adding syrup B to it.From the resultant solution 30aliter is withdrawn and then replaced with B. The resultant ratio of syrup A and B in final solution is 3:7. Find original volume of solution
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Volume of syrup B = x Volume of syrup A = 1.5 x as ratio 3:2.
Total volume V = x + 1.5 x = 2.5 x Liters
New volume of mixture = 1.50 V = 3.75 x
Volume of B in that = x + V/2 = x + 1.25 x = 2.25 x
So volume of A in that still = 1.50 x
Ratio of A : B in the mixture = 1.50 x : 2.25 x = 2 : 3
30 L is removed. So total Volume becomes V2 = 3.75 y - 30 L
Volume of syrup A removed = 2/(2+3) * 30 L = 12 L
Volume of syrup B removed = 3/(2+3) * 30 L = 18 L
New volume of A = 1.5 x - 12 L
New volume of B = 2.25 x - 18 L
Amount of syrup B added: 30 L
New Volume of B in the mixture = 2.25 x + 12 L
Ratio of Syrup A : B = (1.5x - 12) : (2.25 x + 12) = 3 : 7
so we get 7 (1.5 x - 12) = 3 ( 2.25 x + 12 )
3.75 x = 120
x = 32
So original volume of Solution = V = 2.5 x = 80 Liters
Total volume V = x + 1.5 x = 2.5 x Liters
New volume of mixture = 1.50 V = 3.75 x
Volume of B in that = x + V/2 = x + 1.25 x = 2.25 x
So volume of A in that still = 1.50 x
Ratio of A : B in the mixture = 1.50 x : 2.25 x = 2 : 3
30 L is removed. So total Volume becomes V2 = 3.75 y - 30 L
Volume of syrup A removed = 2/(2+3) * 30 L = 12 L
Volume of syrup B removed = 3/(2+3) * 30 L = 18 L
New volume of A = 1.5 x - 12 L
New volume of B = 2.25 x - 18 L
Amount of syrup B added: 30 L
New Volume of B in the mixture = 2.25 x + 12 L
Ratio of Syrup A : B = (1.5x - 12) : (2.25 x + 12) = 3 : 7
so we get 7 (1.5 x - 12) = 3 ( 2.25 x + 12 )
3.75 x = 120
x = 32
So original volume of Solution = V = 2.5 x = 80 Liters
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the answer is 80. if there is a trick please let me know
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