Question

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 The volume of contents is increased by 50% by adding syrup B to it.From the resultant solution 30aliter is withdrawn and then replaced with B. The resultant ratio of syrup A and B in final solution is 3:7.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

Answer 1

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

Answer 2

the answer is 80. if there is a trick please let me know