MAT Exam 2025 Paper

Concept:Each time some juice is removed and replaced with water, the remaining juice is multiplied by the fraction left after one draw.Explanation:Let the initial quantity of juice be $x$ ml.In one operation, $\frac{1}{6}$ of the juice is drawn out.So the fraction of juice remaining after each operation is:$$1 - \frac{1}{6} = \frac{5}{6}$$After 3 such operations, the fraction of original juice left is:$$\left(\frac{5}{6}\right)^3 = \frac{125}{216}$$Given that this remaining juice is $1250$ ml:$$\frac{125}{216} \times x = 1250$$$$x = \frac{1250 \times 216}{125} = 10 \times 216 = 2160 \text{ ml}$$Converting to litres:$$2160 \text{ ml} = 2.160 \text{ ltr}$$Answer:The initial quantity of juice in the jug was $2.160$ ltr.Correct option: D. 2.160 ltr.