**24. Choose the right answer from the four ****alternatives given below:**

**(i) Which one of the following methods of scale is universal method?**

(a) Simple Statement

(b) Representative Fraction

(c) Graphical Scale

(d) None of the above

**Ans.** (b) Representative Fraction

**(ii) Map distance in a scale is also known as:**

(a) Numerator

(b) Denominator

(c) Statement of Scale

(d) Representative Fraction

**Ans.** (a) Numerator

**(iii) ‘Numerator’ in scale represents:**

(a) Ground distance

(b) Map distance

(c) Both the distance

(d) None of the above

**Ans.** (b) Map distance

**25. Answer the following questions in about 30 ****words:**

**(i) What are the two different systems of ****measurement?**

**Ans.** The two different systems of measurement are: Metric and British.

**(ii) Give one example each of statement of scale in Metric and English system.**

**Ans.** **System of Measurement**

1 km = 1000 Metres

1 Metre = 100 Centimetres

1 Centimetre = 10 Millimetres

English System of Measurement

1 Mile = 8 Furlongs

1 Furlong = 220 Yards

1 Yard = 3 feet

1 Foot = 12 Inches.

**(iii) Why is the Representative Fraction method ****called a Universal method?**

**Ans.** It shows the relationship between the map distance and the corresponding ground distance in units of length. The use of units to express the scale makes it the most versatile method. It may, however, be noted that while converting the fraction of units into Metric or English systems, units in centimetre or inch are normally used by convention. This quality of expressing scale in units in R.F. makes it a universally acceptable and usable method.

**(iv) What are the major advantages of the graphical method?**

**Ans.** Following points show the advantages of the graphical method:

(a) It can express scale not only in kilometres and metres but the readings may also be shown in miles and furlongs.

(b) The graphical scale stands valid even when the map is reduced or enlarged. This is the unique advantage of the graphical method of the map scale.

**26. Convert the given Statement of Scale into ****Representative Fraction (R. F.).**

**(i) 5 cm represents 10 km**

**(ii) 2 inches represents 4 miles**

**(iii) 1 inch represents 1 yard**

**(iv) 1 cm represents 100 metres**

**Ans.** (i) Representative Fraction

$$=\frac{\text{Distance of Map}}{\text{Distance of Ground}}$$

Distance on Map = 5 cm

Distance on Ground = 10 km

$$\therefore\space\text{Representative Fraction = }\frac{5}{10}=\frac{1}{2}$$

or 2,00,000 cm

Therefore representative fraction = 1 : 2,00,000 cm

(ii) Representative Fraction

$$=\frac{\text{Distance of Map}}{\text{Distance of Ground}}$$

2 inches = 4 miles

Therefore, 1 inch = 2 miles (63,360 × 2)

1 inch on map = 1, 26,720 inches on ground.

Therefore representative fraction = 1 : 1, 26, 720

(iii) Representative Fraction

$$=\frac{\text{Distance of Map}}{\text{Distance of Ground}}$$

Distance on Map =1 inch

Distance on Ground = 1 yard

1 yard = 36 inches

$$\text{Representative Fraction}=\frac{1}{36}$$

Therefore representative fraction = 1:36

(iv) Representative Fraction

$$=\frac{\text{Distance of Map}}{\text{Distance of Ground}}$$

Distance on Map = 1 cm

Distance on Ground = 100 meters

1 cm = 100 meters

$$\text{Representative Fraction}=\frac{1}{10,000}$$

Therefore representative fraction = 1 : 10,000

**27. Convert the given Representative Fraction ****(R F.) into Statement of Scale in the System of ****Measurement shown in parentheses:**

**(i) 1:1,00,000 (into km)**

**(ii) 1:31680 (into furlongs)**

**(iii) 1:126,720 (into miles)**

**(iv) 1:50,000 (into metres)**

**Ans.** (i) It means 1,00,000 cm on map represents 1 km on ground.

It means 1,00,000 centimetre on map represents 1,00,000 cm on ground. Therefore, 1 cm represents 1 km

(ii) 1 inch represents 31,680 inches

1 mile = 8 furlongs

1 furlong = 220 yards

1 yard = 3 feet

1 foot = 12 inches

Therefore, 31680 inches = 31680 divided by 12 × 3 × 220 furlongs = 4 furlongs

Therefore, 31680 inches = 4 furlongs

(iii) 1 inch represents 1,26,720 inches

1 mile = 63,360 inches

Therefore, 1,26,720 inches = 2 miles

Hence, 1 inch represents 2 miles

(iv) 1 cm represents = 50,000 em

1 metre = 100 cm

Therefore, 1 cm represents 500 metres

**28. Construct a graphical scale when the given R. F. is 1:50,000 and read the distances in kilometre and metre.**

**Ans.** According to a standard, generally a length of 15 cm is taken to draw a graphical scale. 1:50,000 means that 1 cm on map shows 50,000 cm on ground. In other words, 1 cm shows 50,000 cm.

15 cm shows 50,000 × 15/1,00,000

15 cm = 7.5 km

Since 7.5 km is not an integer, so we can round it off to 5 or 10. Let us round it off to 5 km.

Therefore, we need to make following calculations to express the scale on a length of 5km. 7 .5 km is shown by 15 cm line.

Therefore, for 5 km we can express it as 15 × 5/7.5 0.5 km will be shown by 1 cm on line. We can make the graph by following steps:

First of all draw a 10 cm line and divide it in 5 important parts. Except one part from the left, let us give all parts a distance of one km. Now divide the first part in 10 equal parts and each part will be equal to 100 metres. We can divide it in five parts as well and taking one part as 200 metre and so on.

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