All the questions from the Exercise at the end of NCERT’s Practical Work in Geography Chapter 2, “Map Scale” (Chapter 22 on this site), in the exact order and wording as printed in the book (English edition), with a full solution to every question. The book does not print answers to these questions; every solution here is worked out using the chapter’s own method. Try solving each one yourself first, then check.
1 Choose the right answer from the four alternatives given below
Q. Which one of the following methods of scale is a universal method?
(a) Simple Statement (b) Representative Fraction (c) Graphical Scale (d) None of the above
Answer: (b) Representative Fraction. The Representative Fraction (R.F.) does not mention the unit of scale, so it can be converted and read in either the Metric or the English system of measurement: this is what makes it the most suitable and universal method.
Q. Map distance in a scale is also known as:
(a) Numerator (b) Denominator (c) Statement of Scale (d) Representative Fraction
Answer: (a) Numerator. In the Representative Fraction, the numerator (the number above the line in the fraction, always 1 unit) represents the distance given on the map; the actual ground distance is called the denominator.
Q. ‘Numerator’ in scale represents:
(a) Ground distance (b) Map distance (c) Both the distances (d) None of the above
Answer: (b) Map distance. In a Representative Fraction (such as 1:24,000), the numerator ‘1’ always represents 1 unit of the given distance on the map, while the denominator (24,000) represents that same number of units as the actual ground distance.
2 Answer the following questions in about 30 words
Q. What are the two different systems of measurement?
Answer: The two systems of measurement are: the Metric System, which uses kilometre-metre-centimetre units and is used in India and many other countries of the world; and the English System, which uses mile-furlong-yard-foot units and is prevalent in the United States and the United Kingdom. India used the English System before 1957.
Q. Give one example each of statement of scale in Metric and English system.
Answer: Statement of Scale in the Metric System: “1 centimetre represents 10 kilometres”, i.e. a distance of 1 cm on the map equals a ground distance of 10 km. In the English System: “1 inch represents 10 miles”, i.e. 1 inch on the map equals 10 miles on the ground.
Q. Why is the Representative Fraction method called a Universal method?
Answer: The Representative Fraction does not mention the unit of scale, so it can be taken in any unit (millimetre, centimetre or inch). For this reason, a person familiar with the Metric System can read it in centimetres and a person familiar with the English System can read it in inches, both equally correctly. For example, R.F. 1:36,000 can be read as both ‘1 cm represents 360 metres’ and ‘1 inch represents 1,000 yards’. This is why it is called the universal method.
Q. What are the major advantages of the graphical method?
Answer: The biggest advantage of the Graphical (bar) scale is that it stays valid even when the map is enlarged or reduced (photocopied, or printed at a different size), because being a line, it enlarges or reduces proportionally along with the map itself, whereas a Statement of Scale has to be reworked in such a case. It is used to read distances directly in units such as kilometres/metres or miles/furlongs.
3 Convert the given Statement of Scale into Representative Fraction (R. F.)
Q. 5 cm represents 10 km
Answer: 10 km = 10 × 100,000 = 1,000,000 cm. This distance is represented by 5 cm, so 1 cm = 1,000,000 ÷ 5 = 200,000 cm. R.F. = 1:200,000
Q. 2 inches represents 4 miles
Answer: 4 miles = 4 × 63,360 = 253,440 inches (since 1 mile = 63,360 inches). This distance is represented by 2 inches, so 1 inch = 253,440 ÷ 2 = 126,720 inches. R.F. = 1:126,720
Q. 1 inch represents 1 yard
Answer: 1 yard = 36 inches (1 yard = 3 feet = 36 inches). A distance of 1 inch on the map represents a ground distance of 36 inches. R.F. = 1:36
Q. 1 cm represents 100 metres
Answer: 100 metres = 100 × 100 = 10,000 cm (1 metre = 100 cm). A distance of 1 cm on the map represents a ground distance of 10,000 cm. R.F. = 1:10,000
4 Convert the given Representative Fraction (R. F.) into Statement of Scale in the System of Measurement shown in parentheses
Q. 1 : 100,000 (into km)
Answer: 1 cm = 100,000 cm. To convert into kilometres, divide by 100,000 (1 km = 100,000 cm): 100,000 ÷ 100,000 = 1. The statement of scale is: 1 cm represents 1 km.
Q. 1 : 31680 (into furlongs)
Answer: 1 inch = 31,680 inches. 1 furlong = 220 yards = 220×3×12 = 7,920 inches. 31,680 ÷ 7,920 = 4. The statement of scale is: 1 inch represents 4 furlongs.
Q. 1 : 126,720 (into miles)
Answer: 1 inch = 126,720 inches. To convert into miles, divide by 63,360 (inches in a mile): 126,720 ÷ 63,360 = 2. The statement of scale is: 1 inch represents 2 miles.
Q. 1 : 50,000 (into metres)
Answer: 1 cm = 50,000 cm. To convert into metres, divide by 100 (cm in a metre): 50,000 ÷ 100 = 500. The statement of scale is: 1 cm represents 500 metres.
5 Construction of the Graphical/Bar Scale
Q. Construct a graphical scale when the given R. F. is 1 : 50,000 and read the distances in kilometre and metre.
Answer: This is the exact same R.F. (1:50,000) that the chapter’s own main text constructs in full as Problem 1. The solution here follows that same method:
1:50,000 means that 1 unit of distance on the map represents 50,000 units on the ground, i.e. 1 cm represents 50,000 cm. Taking a conventional length of about 15 cm: 15 cm = 50,000 × 15 ÷ 100,000 = 7.5 km. Since 7.5 (km) is not a round number, the nearest round number, 5 km, is taken. The new length of the line for 5 km: 15 × 5 ÷ 7.5 = 10 cm.
Construction: First, draw a straight line of 10 cm and divide it into 5 equal main parts. Leaving out one main part on the left, give each of the remaining parts a value of 1 km, starting from 0 towards the right. Now divide the left-hand part of the line into 10 equal sub-divisions, and starting from 0, mark each sub-division with a value of 100 metres (alternatively, it can be divided into 2, 4 or 5 parts, each sub-division given a value of 500, 250 or 200 metres respectively). On the 10 cm graphical scale built this way, whole kilometres can be read on the right and sub-kilometre distances up to 100 m on the left.
Questions 3 and 4 of the exercise are asked directly as numericals in the exam. Instead of memorising R.F. values, remember these four conversion numbers every time: 1 mile = 63,360 inches, 1 kilometre = 100,000 centimetres, 1 metre = 100 centimetres, and 1 furlong = 7,920 inches: each sub-part of Questions 3, 4 and 5 can be solved using just these four.