Extend ratio and proportion to maps, ratios with more than two terms, dividing quantities in a given ratio, pie charts, and inverse proportion.
Map scales express a ratio between distance on a map and real-world distance. Ratios can also involve more than two terms, like dividing something among three or more shares.
A map has scale 1:50,000. If two towns are 6 cm apart on the map, find the real distance.
6×50,000 = 3,00,000 cm = 3 km
Divide ₹900 among three friends in the ratio 1:2:3.
Total parts=6; each part=150; shares are ₹150, ₹300, ₹450
In inverse proportion, as one quantity increases, the other decreases proportionally, so their product stays constant.
If 4 workers finish a job in 15 days, how many days would 6 workers take?
4×15=6×d → d=60/6=10 days
A car travels at 60 km/h and takes 5 hours. At what speed would it take 4 hours for the same distance?
60×5=speed×4 → speed=300/4=75 km/h
1. A map has scale 1:25,000. If two points are 8 cm apart on the map, find the real distance.
2. Divide ₹1,500 among three people in the ratio 2:3:5.
3. If 5 machines complete a task in 12 hours, how many hours would 10 machines take?
4. A pie chart shows a budget: Food 40%, Rent 35%, Savings 25%. If the total budget is ₹40,000, find the amount for Rent.
5. If 8 pipes fill a tank in 6 hours, how many hours would 4 pipes take?