Question
A container has β2xβ litres of juice and β3yβ
litres of soda. If 24 litres of soda is added to the container, the ratio of juice to soda becomes 5:6. However, if only 12 litres of soda is added, the ratio of soda to juice becomes 3:5. What is the original quantity of juice in the container?Solution
ATQ,
{2x / (3y + 24)} = 5/6 β 12x = 15y + 120 β 4x β 5y = 40 β¦β¦(1) Also, {(3y + 12) / 2x} = 3/5 β 5(3y + 12) = 6x β 15y + 60 = 6x β 6x β 15y = 60 β¦β¦(2) Now, (1) Γ 3: 12x β 15y = 120 (2): 6x β 15y = 60 Subtracting: 6x = 60 x = 10 β΄ Initial juice = 2x = 2 Γ 10 = 20 litres
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