In a blend of 183 liters consisting of juice and honey, the quantity of juice exceeds that of honey by 69 liters. When two-third of the mixture is substituted with 'L' liters of honey, the resulting blend contains 60% juice. Determine the value of 'L'.

Solution

ATQ, Let the quantity of Honey in the 183 litres mixture = ‘h’ liters Then, quantity of Juice in the 183 litres mixture = (h + 69) liters We have h + h + 69 = 2h + 69 = 183 So, h = (183 – 69) ÷ 2 = 57 So, ratio of quantity of juice to that of honey in 183 ml of mixture = (57 + 69):(57) = 42:19 Quantity of juice left after removing (1/3)rd of the mixture = 183 × (2/3) × (42/61) = 84 liters Quantity of honey left after removing (1/3)rd of the mixture = 183 × (2/3) × (19/61) = 38 liters ATQ, 84 ÷ (84 + 38 + L) = 0.6 Or, (122 + L) × 0.6 = 84 Or, 73.2 + 0.6L = 84 Or, 73.2 + 0.6L = 84 Or, L = (84 – 73.2) ÷ 0.6 = 18