Understand how two quantities can grow together or work against each other, and use that relationship to solve problems.
Two quantities are in direct variation if they increase or decrease together at the same rate — their ratio stays constant. If x and y vary directly, then x/y = constant, or y = kx for some constant k.
If 5 books cost ₹250, find the cost of 8 books (assuming direct variation).
Cost per book = 250/5 = 50; 8 books = 50 × 8 = ₹400
If y varies directly with x, and y = 12 when x = 4, find y when x = 10.
k = 12/4 = 3, so y = 3 × 10 = 30
Two quantities are in inverse variation if one increases as the other decreases, keeping their product constant. If x and y vary inversely, then x × y = constant.
If 6 workers can finish a job in 10 days, how many days would 4 workers take (assuming inverse variation)?
6 × 10 = 60 (constant); 4 workers: 60 ÷ 4 = 15 days
If y varies inversely with x, and y = 8 when x = 3, find y when x = 6.
k = 8 × 3 = 24; y = 24 ÷ 6 = 4
1. If 4 pens cost ₹60, find the cost of 7 pens (direct variation).
2. If y varies directly with x, and y = 20 when x = 5, find y when x = 8.
3. If 8 workers can complete a job in 12 days, how many days would 6 workers take (inverse variation)?
4. If y varies inversely with x, and y = 10 when x = 4, find y when x = 5.
5. A car travels at a constant speed. If it covers 150km in 3 hours, how far will it travel in 5 hours (direct variation)?