Convert the given Statement of Scale into Representative Fraction
(R. F.).
5 cm represents 10 km
2 inches represents 4 miles
1 inch represents 1 yard
1 cm represents 100 metres
Answers
The given statements of scale can be converted into their respective representative fraction as follows :
(i) 1 : 2,00,000
(ii) 1 : 1,26,720
(iii) 1 : 36
(iv) 1 : 10,000
• 5 cm represents 10 km
1 km = 1000 m, and 1 m = 100 cm.
=> 1 km = 1000 × 100 cm = 100000 cm
=> 10 km = 10 × 100000 cm = 1000000 cm
According to the given scale, 5 cm represents 10 km.
=> 5 cm represents 1000000 cm on ground
=> 1 cm represents (1000000 / 5) cm on ground
Or, 1 cm represents 2,00,000 cm
∴ The representative fraction of the scale is 1 : 2,00,000.
This means that 1 cm on map represents 2,00,000 cm on ground.
• 2 inches represents 4 miles
1 mile = 63360 inches
=> 4 miles = 4 × 63360 inches = 253440 inches
According to the given scale, 2 inches represents 4 miles.
=> 2 inches represents 2,53,440 inches
=> 1 inch on map represents (2,53,440 / 2) inches on ground
Or, 1 inch on map represents 1,26,720 inches on ground.
∴ The representative fraction of the scale is 1 : 1,26,720.
• 1 inch represents 1 yard
1 yard = 36 inches
According to the given scale, 1 inch represents 1 yard.
=> 1 inch on map represents 36 inches on ground
∴ The representative fraction of the scale is 1 : 36.
• 1 cm represents 100 metres
1 m = 100 cm
=> 100 m = 100 × 100 cm
Or, 100 m = 10,000 cm
According to the given scale, 1 cm represents 100 m.
=> 1 cm on map represents 10,000 cm on ground
∴ The representative fraction of the scale is 1 : 10,000.
According to the given scale, 5 cm represents 10 km. ∴ The representative fraction of the scale is 1 : 2,00,000. This means that 1 cm on map represents 2,00,000 cm on ground. According to the given scale, 2 inches represents 4 miles.