| --- |
| source: ncert |
| topic: arithmetic |
| class_level: class_8 |
| chapter: ch13 |
| difficulty: beginner |
| --- |
| |
| Class 8 | Ch13: Direct and Inverse Proportion |
| DIRECT PROPORTION: |
| x and y are in direct proportion if x/y=k (constant) or x1/y1=x2/y2. |
| As x increases, y increases proportionally. Symbol: x∝y. |
| Graph: straight line through origin. |
| Examples: cost∝quantity, distance∝time(constant speed), simple interest∝time. |
| INVERSE PROPORTION: |
| x and y are in inverse proportion if xy=k (constant) or x1×y1=x2×y2. |
| As x increases, y decreases proportionally. Symbol: x∝1/y. |
| Graph: hyperbola (not straight line). |
| Examples: speed∝1/time, workers∝1/days, pipes∝1/fill time. |
| SOLVED EXAMPLES: |
| Example 1 (Direct): If 15 bags of rice cost ₹450, find cost of 24 bags. |
| 15/450=24/x → x=24×450/15=₹720. OR cost per bag=30, 24×30=720. |
| Example 2 (Inverse): 8 workers finish in 12 days. How many days for 6 workers? |
| 8×12=6×d → d=96/6=16 days. (fewer workers → more days → inverse) |
| Example 3 (Inverse): 3 pipes fill tank in 8 hours. How long for 4 pipes? |
| 3×8=4×t → t=24/4=6 hours. |
| Example 4: Car travels 150km in 3 hours. How long for 250km at same speed? |
| 3/150=t/250 → t=500/100=5 hours. (direct proportion) |
| IDENTIFYING TYPE: |
| More→More: Direct proportion. |
| More→Less: Inverse proportion. |
| Workers and days: MORE workers, LESS days → INVERSE. |
| Speed and time: MORE speed, LESS time → INVERSE. |
| COMMON MISTAKES: |
| Workers and days is INVERSE not direct. |
| In inverse proportion: x1×y1=x2×y2 (NOT x1/y1=x2/y2). |
