Concepts of Physics

IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions

A puzzle with Volume

Introduction

Getting a feeling of the volume is important. Normally, litre is used to measure the volume. Conversion to other units is 1 l= 1000 ml.

Apparatus

Three containers of volumes 300 ml, 500 ml, and 800 ml.

Procedure

Take three containers of volumes 300 ml, 500 ml, and 800 ml. Fill the 800 ml container with water. Now divide this water in two equal parts i.e., 400 ml and 400 ml using given containers only.

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Discussion

This is one of the common puzzle in mathematics. There are various methods to solve this e.g., hit and trial method, logical method etc. The steps involved in logical method are:

  1. Arrange the three containers such that volume is in descending order.
  2. Transfer from highest to medium if medium is empty.
  3. Transfer from medium to least if least is not fully filled.
  4. Transfer from least to highest if least is filled.

The students may be asked to measure mass of the water and find its density.

Note

We can also use containers of 1000 ml, 700 ml and 300 ml.