Number of bacteria in a container doubles in every one minute. If the container gets completely filled with bacteria in 30 minutes, then in how many minutes 1/4^th of the container shall be filled with bacteria?

Question

Question

This question was previously asked in

UGC NET Paper 1: Held on 30 Sep 2022 Shift 1

Answer 1

Given

The container gets completely filled with bacteria = 30 minutes

Concept

Every 1 minute = Number of bacteria in a container doubles

Solution

No. of bacteria intially in the cup =1

After 1 min no. of cells will be 2×1=2¹

After 2 min = 2×2 = 2²

After 3 min = 2×2×2 = 2³

So, after 30 min no. of cells will be 2³⁰

Quantity of whole cup = 230 cells

Quantity of 1/4th a cup = 230/2² = 2²⁸

Thus, time taken to fill half of the cup = 28 min

Hence, it will be 1/4th in 28 minutes.