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Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation
7.3 Representative Ratio

Representative Ratio = Distance in a drawing or sketch : Actual distance on the ground.

Example: A sketch is drawn to the scale 1 cm = 2 km, find the representative ratio.

The scale on the sketch is,1 cm = 2 km.
First, make all the units consistent, i.e., change 2 km into cm.
i.e., 2 km = 2 x 1000m x 100cm = 200,000 cm.
Therefore, the Representative Ratio = 1 : 200,000


Directions: Answer the following questions. Also write at least ten examples of your own.
Q 1: The Representative Ratio of a map is 1:4,000,000. In this map, the distance between Los Angeles and Chicago is 42 cm; and the distance between Detroit and New York is 30 cm. What is the actual distances between these pairs of cities?
2100 km and 1860 km respectively
1200 km and 1680 km respectively
1680 km and 1200 km respectively
1860 km and 2100 km respectively

Q 2: Distance between Los Angeles and San Fransisco is 360 km. In a map, this distance is shown as 1.8 cm. Find the Representative Ratio of the map.
200,000:1
1.8:360
1:200,000
360:1.8

Q 3: The minimum distance between two cities is 40 km, what will be the distance between them in a map with Representative Ratio of 1:200,000?
20 cm
30 cm
4 cm
40 cm

Q 4: The length of a bridge is 2631 m. What will be its length in a map with a Representative Ratio of 1:100,000?
26.31 cm
1.0 cm
2.631 cm
2.563 cm

Q 5: In a map with Representative Ratio of 1:8,000,000, the length of a river is 82.2 cm. Find its actual length.
7324 km
4578 km
6656 km
5656 km

Q 6: Area of Lake Superior is 81,460 sq km. What will be its area in a map drawn with a Representative Ratio of 1:4,000,000?
45.64 sq cm
55.96 sq cm
50.91 sq cm
58.36 sq cm

Q 7: The height of Mt. Kanchanganga is 8.58 km. What will be its height in a map with Representative Ratio of 1:250,000?
34.2 cm
3.432 cm
3.500 cm
2.5 cm

Q 8: In a map with Representative Ratio of 1:5,000,000, the distance between two landmarks is 12.9 cm. What is the actual distance between the two landmarks?
546 km
359 km
645 km
784 km

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Question 10: This question is available to subscribers only!


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