Question 14.

A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is

A
B
C
D

Question Explanation

Text Explanation

Let's assume that after n iteration, the volume of the milk will be less than 50%, which is less than 20 liters.

Initially, the amount of milk is 40 liters, after the first iteration, the volume of milk is 40910 40 \cdot \frac{9}{10}

After the second iteration, the volume of milk is 40×(910)2 40 \times \left(\frac{9}{10}\right)^2

Similarly, after the n iterations, the volume of milk is 40×(910)n 40 \times \left(\frac{9}{10}\right)^n

Now,

40×(910)n20 40 \times \left(\frac{9}{10}\right)^n \leq 20

=> (910)n12 \left(\frac{9}{10}\right)^n \leq \frac{1}{2}

=> n7 n \geq 7

Hence, the correct answer is 7

Video Explanation
XAT 2026 Full Course - Enroll Now for Best XAT Preparation
CAT LRDI 100 Recorded Course - Master Logical Reasoning and Data Interpretation
HOME
XAT Sankalp Sale
Quant Revision Book
More
YoutubeWhatsapp