MAT Exam 2024 Paper

Concept:Use the mixture rule: the sugar content in the final solution equals the sum of sugar from both solutions divided by the total volume.Explanation:Let $x$ litres of the second solution be added to $20$ litres of the first solution.Sugar in the first solution $= 20\%$ of $20 = 4$ litres.Sugar in the second solution $= 10\%$ of $x = 0.1x$ litres.Total volume of the mixture $= 20 + x$ litres.The final mixture must contain $15\%$ sugar, so:$$4 + 0.1x = 0.15(20+x)$$Solving:$$4 + 0.1x = 3 + 0.15x$$$$1 = 0.05x$$$$x = 20$$Verification: mixing $20$ L of $20\%$ syrup with $20$ L of $10\%$ syrup gives $6$ L sugar in $40$ L solution, which is $15\%$.Answer:$20$ litres (Option D)