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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). |