A town planner measures 2000mm on a map of scale 1:500 and for the same distance on a map of unknown scale, she measures 500mm. What is the scale of the second map?
If the scale on the first map is increased by 20% what is the new scale
To find the scale of the second map, we can set up a proportion with the distance measured on both maps.
On the first map, the distance is 2000mm with a scale of 1:500.
On the second map, the distance is 500mm with an unknown scale.
Let x represent the scale of the second map.
The proportion can be set up as:
2000mm/500mm = 1:500/x
Cross multiplying gives:
2000x = 500 * 500
Simplifying gives:
2000x = 250000
Dividing both sides by 2000 gives:
x = 250000 / 2000
x = 125
So, the scale of the second map is 1:125.
To find the new scale if the scale on the first map is increased by 20%, we can simply multiply the original scale by 1.2.
Original scale: 1:500
New scale: 1.2 * 1:500
New scale: 1:600
The new scale is 1:600.
To find the scale of the second map, we can set up a ratio using the measurements on both maps.
On the first map, the distance is 2000mm and the scale is 1:500.
On the second map, the distance is 500mm and the scale is unknown.
We can set up the ratio as follows:
2000mm (first map) / 1:500 (first map scale) = 500mm (second map) / x (unknown scale)
Cross-multiplying, we get:
2000mm * x = 500mm * 1:500
Simplifying, we have:
2000x = 500
Dividing both sides by 2000, we get:
x = 500 / 2000
x = 1:4
Therefore, the scale of the second map is 1:4.
Now, let's calculate the new scale if the scale on the first map is increased by 20%.
The original scale on the first map is 1:500.
To increase it by 20%, we add 20% of 500 (which is 100) to the original scale.
So the new scale would be 1:500 + 100 = 1:600.
To find the scale of the second map, we can use the concept of ratios. The scale of a map represents the relationship between distances on the map and the actual distances on the ground.
Let's set up a ratio using the measurements on the first map: 1:500. This means that 1 unit on the map represents 500 units on the ground. In this case, the town planner measures 2000mm on the first map, so we can set up the following equation:
1 unit (on the first map) / 500 units (on the ground) = 2000mm (on the first map) / x mm (on the ground, for the second map)
By cross-multiplying and solving for x, we can determine the scale of the second map. Here's the equation:
1 * x = 500 * 2000
x = 1,000,000mm
Therefore, the scale of the second map is 1:1,000,000. This means that 1 unit on the second map represents 1,000,000 units on the ground.
Now, let's move on to the second question about increasing the scale of the first map by 20%.
To find the new scale, we first need to calculate the increase in the scale. If the scale is increased by 20%, it means the original scale is multiplied by 1 + 20% (or 0.2). So, the new scale can be calculated as:
New Scale = Original Scale * (1 + Percentage Increase)
In this case, the original scale is 1:500. Applying the formula, we get:
New Scale = 1:500 * (1 + 0.20) = 1:500 * 1.20 = 1:600.
Therefore, the new scale of the first map, after increasing it by 20%, is 1:600.