Question
The ratio of the quantity of juice and water in vessel A
and vessel B is 3:2 and 4:3 respectively. 45 liters of mixture is taken out from vessel A and poured into vessel B. After this, the ratio of juice and water in vessel B becomes 19:14. The initial quantity of juice in vessel A is equal to the difference between the final quantity of juice and water in vessel B. Find the initial total quantity of mixture in vessel A.Solution
ATQ, In vessel A, Juice = 3x Water = 2x In vessel B, Juice = 4y Water = 3y From vessel A, 45 liters is removed. Total parts in A = 3 + 2 = 5 Juice removed = 45 × 3/5 = 27 liters Water removed = 45 × 2/5 = 18 liters In vessel B after mixing: Final juice = 4y + 27 Final water = 3y + 18 Given final ratio: (4y + 27)/(3y + 18) = 19/14 14(4y + 27) = 19(3y + 18) 56y + 378 = 57y + 342 y = 36 Final juice in B = 4×36 + 27 = 144 + 27 = 171 liters Final water in B = 3×36 + 18 = 108 + 18 = 126 liters Difference = 171 – 126 = 45 Given: initial juice in A = difference ⇒ 3x = 45 x = 15 Total mixture in A initially = (3x + 2x) = 5x = 5 × 15 = 75 liters
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