Question
A 315 ml mixture contains honey
and water in the ratio of ______. If 60% of this mixture is removed, and then ____ ml of honey along with 56 ml of water is added to what remains, the new ratio of honey to water becomes ______. Which set of values can fill the blanks in that order? I) 5:4, 98, 3:2 II) 3:2, 57.4, 5:4 III) 4:3, 48, 12:11Solution
ATQ,
For case I: Honey in 315 ml mixture = (5/9) × 315 = 175 ml Water in 315 ml mixture = 315 – 175 = 140 ml Required ratio = (0.40 × 175 + 98) : (0.40 × 140 + 56) = 168 : 112 = 3 : 2 Therefore, option I is possible. For case II: Honey in 315 ml mixture = (3/5) × 315 = 189 ml Water in 315 ml mixture = 315 – 189 = 126 ml Required ratio = (0.40 × 189 + 57.4) : (0.40 × 126 + 56) = 133 : 106.4 = 5 : 4 Therefore, option II is possible. For case III: Honey in 315 ml mixture = (4/7) × 315 = 180 ml Water in 315 ml mixture = 315 – 180 = 135 ml Required ratio = (0.40 × 180 + 48) : (0.40 × 135 + 56) = 120 : 110 = 12 : 11 Therefore, option III is possible.
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